Properties

Label 8281.2.a
Level $8281$
Weight $2$
Character orbit 8281.a
Rep. character $\chi_{8281}(1,\cdot)$
Character field $\Q$
Dimension $502$
Newform subspaces $78$
Sturm bound $1698$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 78 \)
Sturm bound: \(1698\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8281))\).

Total New Old
Modular forms 904 557 347
Cusp forms 793 502 291
Eisenstein series 111 55 56

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

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(118\)
\(+\)\(-\)\(-\)\(130\)
\(-\)\(+\)\(-\)\(131\)
\(-\)\(-\)\(+\)\(123\)
Plus space\(+\)\(241\)
Minus space\(-\)\(261\)

Trace form

\( 502 q - 4 q^{3} + 472 q^{4} + 2 q^{5} + 12 q^{8} + 442 q^{9} + O(q^{10}) \) \( 502 q - 4 q^{3} + 472 q^{4} + 2 q^{5} + 12 q^{8} + 442 q^{9} + 6 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{15} + 416 q^{16} + 4 q^{18} - 12 q^{19} - 2 q^{20} + 14 q^{22} + 6 q^{23} - 4 q^{24} + 404 q^{25} + 2 q^{27} + 20 q^{29} + 58 q^{30} - 4 q^{31} + 44 q^{32} - 4 q^{33} + 2 q^{34} + 354 q^{36} + 16 q^{37} - 20 q^{38} + 14 q^{40} + 2 q^{41} + 22 q^{43} + 28 q^{44} + 22 q^{45} + 8 q^{46} + 8 q^{47} + 46 q^{48} + 40 q^{50} + 6 q^{51} + 16 q^{53} + 48 q^{54} + 16 q^{55} + 16 q^{57} + 40 q^{58} + 16 q^{59} - 24 q^{61} - 10 q^{62} + 318 q^{64} + 26 q^{66} + 90 q^{68} - 16 q^{69} - 28 q^{71} + 40 q^{72} - 22 q^{73} + 70 q^{74} - 54 q^{75} + 16 q^{76} + 34 q^{79} - 38 q^{80} + 246 q^{81} + 52 q^{82} + 24 q^{83} + 24 q^{85} - 52 q^{86} + 16 q^{87} + 42 q^{88} + 26 q^{89} + 28 q^{90} - 140 q^{92} + 28 q^{93} - 2 q^{94} + 22 q^{95} - 4 q^{96} - 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8281))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13
8281.2.a.a 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-2\) \(-2\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.b 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-2\) \(2\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.c 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(-3\) \(-3\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots\)
8281.2.a.d 8281.a 1.a $1$ $66.124$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
8281.2.a.e 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.f 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.g 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(3\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots\)
8281.2.a.h 8281.a 1.a $1$ $66.124$ \(\Q\) None \(0\) \(2\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots\)
8281.2.a.i 8281.a 1.a $1$ $66.124$ \(\Q\) None \(1\) \(-3\) \(3\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots\)
8281.2.a.j 8281.a 1.a $1$ $66.124$ \(\Q\) None \(1\) \(3\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots\)
8281.2.a.k 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(-2\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.l 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(0\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots\)
8281.2.a.m 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(2\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.n 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.o 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.p 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.q 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8281.2.a.r 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.s 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.t 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.u 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots\)
8281.2.a.v 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
8281.2.a.w 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.x 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.y 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.z 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.ba 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.bb 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.bc 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-4\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bd 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
8281.2.a.be 8281.a 1.a $3$ $66.124$ 3.3.148.1 None \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bf 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) None \(-2\) \(2\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bg 8281.a 1.a $3$ $66.124$ 3.3.316.1 None \(-1\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.bh 8281.a 1.a $3$ $66.124$ 3.3.404.1 None \(2\) \(-4\) \(5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bi 8281.a 1.a $3$ $66.124$ 3.3.148.1 None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bj 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) None \(2\) \(2\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bk 8281.a 1.a $3$ $66.124$ 3.3.404.1 None \(2\) \(4\) \(-5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bl 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(3\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots\)
8281.2.a.bm 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(4\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots\)
8281.2.a.bn 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{2}, \sqrt{23})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
8281.2.a.bo 8281.a 1.a $4$ $66.124$ 4.4.105456.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
8281.2.a.bp 8281.a 1.a $4$ $66.124$ 4.4.27004.1 None \(-1\) \(-1\) \(7\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bq 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
8281.2.a.br 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots\)
8281.2.a.bs 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
8281.2.a.bt 8281.a 1.a $4$ $66.124$ 4.4.27004.1 None \(1\) \(-1\) \(-7\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bu 8281.a 1.a $4$ $66.124$ 4.4.105456.1 None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
8281.2.a.bv 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{2}, \sqrt{23})\) None \(4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8281.2.a.bw 8281.a 1.a $5$ $66.124$ 5.5.746052.1 None \(-4\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.bx 8281.a 1.a $5$ $66.124$ 5.5.746052.1 None \(-4\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.by 8281.a 1.a $6$ $66.124$ 6.6.7674048.1 None \(-4\) \(0\) \(6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.bz 8281.a 1.a $6$ $66.124$ 6.6.6995813.1 None \(-2\) \(-1\) \(-1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.ca 8281.a 1.a $6$ $66.124$ 6.6.6995813.1 None \(-2\) \(1\) \(1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cb 8281.a 1.a $6$ $66.124$ 6.6.1279733.1 None \(-2\) \(4\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots\)
8281.2.a.cc 8281.a 1.a $6$ $66.124$ 6.6.4507648.1 None \(0\) \(-8\) \(6\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.cd 8281.a 1.a $6$ $66.124$ 6.6.4507648.1 None \(0\) \(8\) \(-6\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.ce 8281.a 1.a $6$ $66.124$ 6.6.6995813.1 None \(2\) \(-1\) \(1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cf 8281.a 1.a $6$ $66.124$ 6.6.6995813.1 None \(2\) \(1\) \(-1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cg 8281.a 1.a $6$ $66.124$ 6.6.1279733.1 None \(2\) \(4\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.ch 8281.a 1.a $6$ $66.124$ 6.6.7674048.1 None \(4\) \(0\) \(-6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.ci 8281.a 1.a $8$ $66.124$ 8.8.8446345216.1 None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
8281.2.a.cj 8281.a 1.a $8$ $66.124$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.ck 8281.a 1.a $8$ $66.124$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.cl 8281.a 1.a $8$ $66.124$ 8.8.8446345216.1 None \(4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.cm 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cn 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-8\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.co 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cp 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cq 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-8\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.cr 8281.a 1.a $12$ $66.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cs 8281.a 1.a $16$ $66.124$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{7}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
8281.2.a.ct 8281.a 1.a $24$ $66.124$ None \(-1\) \(0\) \(-13\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
8281.2.a.cu 8281.a 1.a $24$ $66.124$ None \(-1\) \(0\) \(13\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
8281.2.a.cv 8281.a 1.a $24$ $66.124$ None \(1\) \(0\) \(-13\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
8281.2.a.cw 8281.a 1.a $24$ $66.124$ None \(1\) \(0\) \(13\) \(0\) $-$ $+$ $\mathrm{SU}(2)$
8281.2.a.cx 8281.a 1.a $32$ $66.124$ None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
8281.2.a.cy 8281.a 1.a $36$ $66.124$ None \(-14\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
8281.2.a.cz 8281.a 1.a $36$ $66.124$ None \(14\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8281))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8281)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)