Properties

Label 8379.2.a
Level $8379$
Weight $2$
Character orbit 8379.a
Rep. character $\chi_{8379}(1,\cdot)$
Character field $\Q$
Dimension $308$
Newform subspaces $76$
Sturm bound $2240$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8379 = 3^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8379.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 76 \)
Sturm bound: \(2240\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8379))\).

Total New Old
Modular forms 1152 308 844
Cusp forms 1089 308 781
Eisenstein series 63 0 63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(28\)
\(+\)\(+\)\(-\)\(-\)\(36\)
\(+\)\(-\)\(+\)\(-\)\(36\)
\(+\)\(-\)\(-\)\(+\)\(24\)
\(-\)\(+\)\(+\)\(-\)\(46\)
\(-\)\(+\)\(-\)\(+\)\(42\)
\(-\)\(-\)\(+\)\(+\)\(45\)
\(-\)\(-\)\(-\)\(-\)\(51\)
Plus space\(+\)\(139\)
Minus space\(-\)\(169\)

Trace form

\( 308 q - q^{2} + 307 q^{4} + 3 q^{5} - 9 q^{8} + O(q^{10}) \) \( 308 q - q^{2} + 307 q^{4} + 3 q^{5} - 9 q^{8} - 2 q^{10} - 3 q^{11} + 6 q^{13} + 289 q^{16} + 13 q^{17} - 2 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 335 q^{25} - 2 q^{26} + 12 q^{29} - 4 q^{31} + 11 q^{32} + 18 q^{34} - 8 q^{37} + 3 q^{38} + 30 q^{40} + 16 q^{41} - 11 q^{43} - 30 q^{44} - 8 q^{46} + 7 q^{47} + q^{50} + 42 q^{52} + 26 q^{53} - 33 q^{55} + 62 q^{58} - 22 q^{59} - 5 q^{61} - 36 q^{62} + 293 q^{64} + 60 q^{65} + 24 q^{67} - 24 q^{68} - 2 q^{71} - 3 q^{73} + 26 q^{74} - 5 q^{76} - 24 q^{79} - 50 q^{80} + 74 q^{82} + 12 q^{83} + 33 q^{85} + 48 q^{86} + 96 q^{88} + 38 q^{89} - 8 q^{92} + 36 q^{94} - 9 q^{95} + 46 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8379))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 19
8379.2.a.a 8379.a 1.a $1$ $66.907$ \(\Q\) None 133.2.f.a \(-2\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-4q^{11}+\cdots\)
8379.2.a.b 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.a \(-2\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-4q^{11}+\cdots\)
8379.2.a.c 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.a \(-2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots\)
8379.2.a.d 8379.a 1.a $1$ $66.907$ \(\Q\) None 133.2.f.a \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-4q^{11}+\cdots\)
8379.2.a.e 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.c \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.f 8379.a 1.a $1$ $66.907$ \(\Q\) None 1197.2.a.b \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-2q^{11}+6q^{13}+\cdots\)
8379.2.a.g 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.c \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+2q^{11}+4q^{13}+\cdots\)
8379.2.a.h 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.b \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{5}+3q^{11}+2q^{13}+4q^{16}+\cdots\)
8379.2.a.i 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.b \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{5}+3q^{11}-2q^{13}+4q^{16}+\cdots\)
8379.2.a.j 8379.a 1.a $1$ $66.907$ \(\Q\) None 19.2.a.a \(0\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
8379.2.a.k 8379.a 1.a $1$ $66.907$ \(\Q\) None 2793.2.a.d \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
8379.2.a.l 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.a \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+2q^{11}-q^{16}+\cdots\)
8379.2.a.m 8379.a 1.a $1$ $66.907$ \(\Q\) None 1197.2.a.b \(1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+2q^{11}+6q^{13}+\cdots\)
8379.2.a.n 8379.a 1.a $1$ $66.907$ \(\Q\) None 2793.2.a.d \(1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
8379.2.a.o 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.b \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
8379.2.a.p 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.a \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}-q^{11}+\cdots\)
8379.2.a.q 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.b \(2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+3q^{11}+\cdots\)
8379.2.a.r 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(-2\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.s 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(-2\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
8379.2.a.t 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
8379.2.a.u 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
8379.2.a.v 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 1197.2.a.f \(-2\) \(0\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{5}+\cdots\)
8379.2.a.w 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{5}) \) None 133.2.a.c \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
8379.2.a.x 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.h \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+\beta q^{11}-2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.y 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.h \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{11}+2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.z 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2\beta q^{5}-2\beta q^{8}-4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.ba 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2\beta q^{5}-2\beta q^{8}+4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.bb 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.f \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots\)
8379.2.a.bc 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-2\beta q^{13}+\cdots\)
8379.2.a.bd 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}+2\beta q^{13}+\cdots\)
8379.2.a.be 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.f \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots\)
8379.2.a.bf 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{13}) \) None 133.2.a.b \(1\) \(0\) \(-6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-3q^{5}+3q^{8}-3\beta q^{10}+\cdots\)
8379.2.a.bg 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 1197.2.a.f \(2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bh 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
8379.2.a.bi 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.c \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bj 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bk 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bl 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.c \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bm 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
8379.2.a.bn 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{5}) \) None 133.2.a.a \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
8379.2.a.bo 8379.a 1.a $3$ $66.907$ 3.3.229.1 None 133.2.a.d \(-2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bp 8379.a 1.a $3$ $66.907$ 3.3.148.1 None 399.2.a.d \(-1\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
8379.2.a.bq 8379.a 1.a $3$ $66.907$ 3.3.404.1 None 399.2.a.e \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.br 8379.a 1.a $4$ $66.907$ 4.4.1957.1 None 399.2.j.d \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bs 8379.a 1.a $4$ $66.907$ \(\Q(\zeta_{24})^+\) None 1197.2.a.n \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
8379.2.a.bt 8379.a 1.a $4$ $66.907$ 4.4.1957.1 None 399.2.j.d \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bu 8379.a 1.a $4$ $66.907$ 4.4.5744.1 None 931.2.a.l \(0\) \(0\) \(-8\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots\)
8379.2.a.bv 8379.a 1.a $4$ $66.907$ 4.4.5744.1 None 931.2.a.l \(0\) \(0\) \(8\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bw 8379.a 1.a $4$ $66.907$ 4.4.13068.1 None 171.2.a.e \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.bx 8379.a 1.a $4$ $66.907$ 4.4.725.1 None 399.2.j.f \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.by 8379.a 1.a $4$ $66.907$ 4.4.725.1 None 399.2.j.f \(2\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.bz 8379.a 1.a $4$ $66.907$ 4.4.23301.1 None 399.2.j.e \(2\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.ca 8379.a 1.a $4$ $66.907$ 4.4.23301.1 None 399.2.j.e \(2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.cb 8379.a 1.a $5$ $66.907$ 5.5.368464.1 None 399.2.a.g \(-3\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8379.2.a.cc 8379.a 1.a $5$ $66.907$ 5.5.1244416.1 None 2793.2.a.bf \(-3\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
8379.2.a.cd 8379.a 1.a $5$ $66.907$ 5.5.1244416.1 None 2793.2.a.bf \(-3\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
8379.2.a.ce 8379.a 1.a $5$ $66.907$ 5.5.1240016.1 None 399.2.a.f \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+(\beta _{2}+\cdots)q^{8}+\cdots\)
8379.2.a.cf 8379.a 1.a $6$ $66.907$ 6.6.39110656.1 None 2793.2.a.bk \(-2\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.cg 8379.a 1.a $6$ $66.907$ 6.6.39110656.1 None 2793.2.a.bk \(-2\) \(0\) \(4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.ch 8379.a 1.a $6$ $66.907$ 6.6.12730624.1 None 1197.2.a.q \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
8379.2.a.ci 8379.a 1.a $6$ $66.907$ 6.6.5163008.1 None 2793.2.a.bi \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots\)
8379.2.a.cj 8379.a 1.a $6$ $66.907$ 6.6.5163008.1 None 2793.2.a.bi \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\beta _{5}q^{5}+\cdots\)
8379.2.a.ck 8379.a 1.a $7$ $66.907$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 133.2.f.d \(-2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}+\beta _{6}q^{5}+\cdots\)
8379.2.a.cl 8379.a 1.a $7$ $66.907$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 133.2.f.d \(-2\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}-\beta _{6}q^{5}+\cdots\)
8379.2.a.cm 8379.a 1.a $8$ $66.907$ 8.8.\(\cdots\).2 None 1197.2.j.n \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
8379.2.a.cn 8379.a 1.a $8$ $66.907$ 8.8.8446345216.1 None 8379.2.a.cn \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}-\beta _{5}q^{4}-\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots\)
8379.2.a.co 8379.a 1.a $8$ $66.907$ 8.8.8446345216.1 None 8379.2.a.cn \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}-\beta _{5}q^{4}+\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots\)
8379.2.a.cp 8379.a 1.a $8$ $66.907$ 8.8.\(\cdots\).2 None 1197.2.j.n \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
8379.2.a.cq 8379.a 1.a $8$ $66.907$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 399.2.j.g \(0\) \(0\) \(-5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
8379.2.a.cr 8379.a 1.a $8$ $66.907$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 399.2.j.g \(0\) \(0\) \(5\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
8379.2.a.cs 8379.a 1.a $10$ $66.907$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 931.2.a.p \(2\) \(0\) \(-16\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{9})q^{5}+\cdots\)
8379.2.a.ct 8379.a 1.a $10$ $66.907$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 931.2.a.p \(2\) \(0\) \(16\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots\)
8379.2.a.cu 8379.a 1.a $12$ $66.907$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1197.2.j.o \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cv 8379.a 1.a $12$ $66.907$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1197.2.j.o \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cw 8379.a 1.a $20$ $66.907$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 8379.2.a.cw \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cx 8379.a 1.a $20$ $66.907$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 8379.2.a.cw \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8379))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8379)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1197))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2793))\)\(^{\oplus 2}\)