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Properties

Label 9282.2.a
Level $9282$
Weight $2$
Character orbit 9282.a
Rep. character $\chi_{9282}(1,\cdot)$
Character field $\Q$
Dimension $191$
Newform subspaces $59$
Sturm bound $4032$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9282.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 59 \)
Sturm bound: \(4032\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9282))\).

Total New Old
Modular forms 2032 191 1841
Cusp forms 2001 191 1810
Eisenstein series 31 0 31

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

\(2\)\(3\)\(7\)\(13\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)$+$\(7\)
\(+\)\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)$+$\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)$+$\(8\)
\(+\)\(+\)\(-\)\(-\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)\(+\)\(+\)$-$\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)$+$\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)$+$\(6\)
\(+\)\(-\)\(+\)\(-\)\(-\)$-$\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)\(-\)$-$\(7\)
\(+\)\(-\)\(-\)\(-\)\(+\)$-$\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)$+$\(5\)
\(-\)\(+\)\(+\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(+\)\(-\)\(-\)$-$\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)$+$\(6\)
\(-\)\(+\)\(-\)\(+\)\(-\)$-$\(6\)
\(-\)\(+\)\(-\)\(-\)\(+\)$-$\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(+\)\(-\)$-$\(8\)
\(-\)\(-\)\(+\)\(-\)\(+\)$-$\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(-\)\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(-\)\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(84\)
Minus space\(-\)\(107\)

Trace form

\( 191 q - q^{2} - q^{3} + 191 q^{4} - 6 q^{5} - q^{6} - q^{7} - q^{8} + 191 q^{9} + O(q^{10}) \) \( 191 q - q^{2} - q^{3} + 191 q^{4} - 6 q^{5} - q^{6} - q^{7} - q^{8} + 191 q^{9} - 6 q^{10} - 12 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 191 q^{16} - q^{17} - q^{18} - 20 q^{19} - 6 q^{20} - q^{21} - 12 q^{22} - 8 q^{23} - q^{24} + 177 q^{25} - q^{26} - q^{27} - q^{28} - 14 q^{29} - 6 q^{30} - 32 q^{31} - q^{32} - 12 q^{33} - q^{34} + 10 q^{35} + 191 q^{36} - 22 q^{37} + 12 q^{38} - q^{39} - 6 q^{40} + 22 q^{41} - q^{42} + 4 q^{43} - 12 q^{44} - 6 q^{45} + 40 q^{46} + 48 q^{47} - q^{48} + 191 q^{49} + 33 q^{50} - q^{51} - q^{52} + 26 q^{53} - q^{54} - 8 q^{55} - q^{56} - 4 q^{57} + 18 q^{58} - 28 q^{59} - 6 q^{60} + 2 q^{61} + 96 q^{62} - q^{63} + 191 q^{64} + 10 q^{65} + 20 q^{66} - 4 q^{67} - q^{68} + 8 q^{69} - 6 q^{70} + 24 q^{71} - q^{72} + 22 q^{73} - 6 q^{74} - 31 q^{75} - 20 q^{76} - 12 q^{77} + 7 q^{78} - 16 q^{79} - 6 q^{80} + 191 q^{81} + 70 q^{82} - 20 q^{83} - q^{84} + 10 q^{85} + 20 q^{86} + 18 q^{87} - 12 q^{88} - 58 q^{89} - 6 q^{90} + 7 q^{91} - 8 q^{92} + 32 q^{94} + 72 q^{95} - q^{96} + 62 q^{97} - q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9282))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 13 17
9282.2.a.a 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.b 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.c 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.d 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
9282.2.a.e 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
9282.2.a.f 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(-1\) \(2\) \(1\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.g 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(-3\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.h 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.i 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.j 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.k 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
9282.2.a.l 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
9282.2.a.m 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.n 9282.a 1.a $1$ $74.117$ \(\Q\) None \(-1\) \(1\) \(3\) \(-1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.o 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.p 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
9282.2.a.q 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
9282.2.a.r 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(-1\) \(4\) \(1\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.s 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(-4\) \(1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.t 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.u 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.v 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.w 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.x 9282.a 1.a $1$ $74.117$ \(\Q\) None \(1\) \(1\) \(4\) \(1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.y 9282.a 1.a $2$ $74.117$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(2\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
9282.2.a.z 9282.a 1.a $2$ $74.117$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(2\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
9282.2.a.ba 9282.a 1.a $3$ $74.117$ 3.3.316.1 None \(-3\) \(-3\) \(-1\) \(-3\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.bb 9282.a 1.a $3$ $74.117$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
9282.2.a.bc 9282.a 1.a $3$ $74.117$ 3.3.6153.1 None \(-3\) \(-3\) \(2\) \(-3\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
9282.2.a.bd 9282.a 1.a $3$ $74.117$ 3.3.257.1 None \(-3\) \(-3\) \(4\) \(3\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
9282.2.a.be 9282.a 1.a $3$ $74.117$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(8\) \(3\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(3-\beta _{1})q^{5}-q^{6}+\cdots\)
9282.2.a.bf 9282.a 1.a $3$ $74.117$ 3.3.473.1 None \(3\) \(-3\) \(0\) \(-3\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.bg 9282.a 1.a $3$ $74.117$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-6\) \(3\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
9282.2.a.bh 9282.a 1.a $3$ $74.117$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-4\) \(3\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
9282.2.a.bi 9282.a 1.a $4$ $74.117$ 4.4.17609.1 None \(-4\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
9282.2.a.bj 9282.a 1.a $4$ $74.117$ 4.4.23665.1 None \(-4\) \(-4\) \(4\) \(4\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{3})q^{5}+q^{6}+\cdots\)
9282.2.a.bk 9282.a 1.a $4$ $74.117$ 4.4.17417.1 None \(-4\) \(4\) \(-2\) \(-4\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.bl 9282.a 1.a $4$ $74.117$ 4.4.17417.1 None \(-4\) \(4\) \(4\) \(-4\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
9282.2.a.bm 9282.a 1.a $4$ $74.117$ 4.4.45841.1 None \(4\) \(-4\) \(-2\) \(4\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
9282.2.a.bn 9282.a 1.a $4$ $74.117$ 4.4.7537.1 None \(4\) \(4\) \(-4\) \(-4\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}+q^{6}+\cdots\)
9282.2.a.bo 9282.a 1.a $4$ $74.117$ 4.4.2777.1 None \(4\) \(4\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}+q^{6}+\cdots\)
9282.2.a.bp 9282.a 1.a $4$ $74.117$ 4.4.26825.1 None \(4\) \(4\) \(2\) \(4\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots\)
9282.2.a.bq 9282.a 1.a $5$ $74.117$ 5.5.218524.1 None \(-5\) \(5\) \(-2\) \(5\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.br 9282.a 1.a $5$ $74.117$ 5.5.176684.1 None \(-5\) \(5\) \(0\) \(5\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.bs 9282.a 1.a $5$ $74.117$ 5.5.1462249.1 None \(5\) \(-5\) \(-7\) \(5\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots\)
9282.2.a.bt 9282.a 1.a $5$ $74.117$ 5.5.3669857.1 None \(5\) \(-5\) \(-3\) \(-5\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
9282.2.a.bu 9282.a 1.a $5$ $74.117$ 5.5.6376252.1 None \(5\) \(-5\) \(2\) \(5\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.bv 9282.a 1.a $6$ $74.117$ 6.6.133576952.1 None \(-6\) \(-6\) \(-2\) \(-6\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.bw 9282.a 1.a $6$ $74.117$ 6.6.298120365.1 None \(-6\) \(6\) \(-4\) \(-6\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1-\beta _{2})q^{5}-q^{6}+\cdots\)
9282.2.a.bx 9282.a 1.a $6$ $74.117$ 6.6.29080364.1 None \(-6\) \(6\) \(0\) \(-6\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots\)
9282.2.a.by 9282.a 1.a $6$ $74.117$ 6.6.314148429.1 None \(6\) \(-6\) \(-2\) \(-6\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{7}+\cdots\)
9282.2.a.bz 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(-1\) \(-7\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.ca 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(1\) \(7\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+q^{7}+\cdots\)
9282.2.a.cb 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(7\) \(1\) \(7\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{7}+\cdots\)
9282.2.a.cc 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(-7\) \(6\) \(-7\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
9282.2.a.cd 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(-7\) \(6\) \(7\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
9282.2.a.ce 9282.a 1.a $7$ $74.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(3\) \(-7\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.cf 9282.a 1.a $8$ $74.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(1\) \(-8\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
9282.2.a.cg 9282.a 1.a $8$ $74.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(3\) \(8\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9282))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9282)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(442))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(663))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1326))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1547))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3094))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4641))\)\(^{\oplus 2}\)