Properties

Label 5775.2.a
Level $5775$
Weight $2$
Character orbit 5775.a
Rep. character $\chi_{5775}(1,\cdot)$
Character field $\Q$
Dimension $188$
Newform subspaces $68$
Sturm bound $1920$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5775.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(1920\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5775))\).

Total New Old
Modular forms 984 188 796
Cusp forms 937 188 749
Eisenstein series 47 0 47

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

\(3\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(13\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(76\)
Minus space\(-\)\(112\)

Trace form

\( 188 q - 4 q^{2} + 176 q^{4} - 8 q^{6} - 12 q^{8} + 188 q^{9} + O(q^{10}) \) \( 188 q - 4 q^{2} + 176 q^{4} - 8 q^{6} - 12 q^{8} + 188 q^{9} - 16 q^{13} + 152 q^{16} - 24 q^{17} - 4 q^{18} - 8 q^{19} + 4 q^{22} + 8 q^{23} - 24 q^{24} + 64 q^{26} + 48 q^{29} - 8 q^{31} - 28 q^{32} + 40 q^{34} + 176 q^{36} + 24 q^{38} + 56 q^{41} + 4 q^{42} + 8 q^{43} + 8 q^{46} + 24 q^{47} + 188 q^{49} - 8 q^{51} - 40 q^{52} - 8 q^{54} + 4 q^{58} + 8 q^{59} + 8 q^{61} + 80 q^{62} + 140 q^{64} + 48 q^{67} + 8 q^{68} - 24 q^{69} + 16 q^{71} - 12 q^{72} - 48 q^{73} + 40 q^{74} - 80 q^{76} + 4 q^{78} - 48 q^{79} + 188 q^{81} + 16 q^{82} + 32 q^{83} - 96 q^{86} + 24 q^{87} - 8 q^{89} - 8 q^{91} + 32 q^{92} - 8 q^{93} + 88 q^{94} + 64 q^{96} - 4 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5775))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7 11
5775.2.a.a 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
5775.2.a.b 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
5775.2.a.c 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
5775.2.a.d 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
5775.2.a.e 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
5775.2.a.f 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
5775.2.a.g 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
5775.2.a.h 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
5775.2.a.i 5775.a 1.a $1$ $46.114$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
5775.2.a.j 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
5775.2.a.k 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
5775.2.a.l 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
5775.2.a.m 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
5775.2.a.n 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
5775.2.a.o 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}+q^{11}-2q^{12}+\cdots\)
5775.2.a.p 5775.a 1.a $1$ $46.114$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
5775.2.a.q 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
5775.2.a.r 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
5775.2.a.s 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
5775.2.a.t 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
5775.2.a.u 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots\)
5775.2.a.v 5775.a 1.a $1$ $46.114$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots\)
5775.2.a.w 5775.a 1.a $1$ $46.114$ \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
5775.2.a.x 5775.a 1.a $1$ $46.114$ \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
5775.2.a.y 5775.a 1.a $1$ $46.114$ \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
5775.2.a.z 5775.a 1.a $1$ $46.114$ \(\Q\) None \(2\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
5775.2.a.ba 5775.a 1.a $1$ $46.114$ \(\Q\) None \(2\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
5775.2.a.bb 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
5775.2.a.bc 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
5775.2.a.bd 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
5775.2.a.be 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
5775.2.a.bf 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
5775.2.a.bg 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots\)
5775.2.a.bh 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+4q^{4}-\beta q^{6}-q^{7}+2\beta q^{8}+\cdots\)
5775.2.a.bi 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
5775.2.a.bj 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots\)
5775.2.a.bk 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
5775.2.a.bl 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{13}) \) None \(1\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
5775.2.a.bm 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{17}) \) None \(1\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
5775.2.a.bn 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{21}) \) None \(1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(3+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
5775.2.a.bo 5775.a 1.a $2$ $46.114$ \(\Q(\sqrt{5}) \) None \(3\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
5775.2.a.bp 5775.a 1.a $3$ $46.114$ 3.3.229.1 None \(-2\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+\cdots\)
5775.2.a.bq 5775.a 1.a $3$ $46.114$ 3.3.316.1 None \(-1\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5775.2.a.br 5775.a 1.a $3$ $46.114$ 3.3.316.1 None \(-1\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.bs 5775.a 1.a $3$ $46.114$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
5775.2.a.bt 5775.a 1.a $3$ $46.114$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
5775.2.a.bu 5775.a 1.a $3$ $46.114$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
5775.2.a.bv 5775.a 1.a $3$ $46.114$ 3.3.148.1 None \(0\) \(3\) \(0\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
5775.2.a.bw 5775.a 1.a $3$ $46.114$ 3.3.837.1 None \(0\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.bx 5775.a 1.a $4$ $46.114$ 4.4.2624.1 None \(-2\) \(4\) \(0\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}-\beta _{3})q^{2}+q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots\)
5775.2.a.by 5775.a 1.a $4$ $46.114$ 4.4.7232.1 None \(-2\) \(4\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\beta _{2}q^{6}+\cdots\)
5775.2.a.bz 5775.a 1.a $4$ $46.114$ 4.4.13448.1 None \(0\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.ca 5775.a 1.a $4$ $46.114$ 4.4.4400.1 None \(0\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cb 5775.a 1.a $4$ $46.114$ 4.4.4400.1 None \(0\) \(4\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5775.2.a.cc 5775.a 1.a $4$ $46.114$ 4.4.2624.1 None \(2\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{3})q^{2}-q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots\)
5775.2.a.cd 5775.a 1.a $5$ $46.114$ 5.5.760752.1 None \(-2\) \(5\) \(0\) \(-5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.ce 5775.a 1.a $5$ $46.114$ 5.5.457904.1 None \(-2\) \(5\) \(0\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cf 5775.a 1.a $5$ $46.114$ 5.5.867696.1 None \(-2\) \(5\) \(0\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cg 5775.a 1.a $5$ $46.114$ 5.5.352076.1 None \(-1\) \(-5\) \(0\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.ch 5775.a 1.a $5$ $46.114$ 5.5.1109184.1 None \(0\) \(-5\) \(0\) \(5\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.ci 5775.a 1.a $5$ $46.114$ 5.5.1109184.1 None \(0\) \(5\) \(0\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cj 5775.a 1.a $5$ $46.114$ 5.5.867696.1 None \(2\) \(-5\) \(0\) \(-5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.ck 5775.a 1.a $5$ $46.114$ 5.5.760752.1 None \(2\) \(-5\) \(0\) \(5\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cl 5775.a 1.a $5$ $46.114$ 5.5.457904.1 None \(2\) \(-5\) \(0\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5775.2.a.cm 5775.a 1.a $10$ $46.114$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(0\) \(-10\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5775.2.a.cn 5775.a 1.a $10$ $46.114$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(0\) \(10\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5775.2.a.co 5775.a 1.a $10$ $46.114$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(10\) \(0\) \(-10\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5775.2.a.cp 5775.a 1.a $10$ $46.114$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(10\) \(0\) \(10\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5775))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\)\(^{\oplus 2}\)