Properties

Label 936.2.g
Level $936$
Weight $2$
Character orbit 936.g
Rep. character $\chi_{936}(469,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $6$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(936, [\chi])\).

Total New Old
Modular forms 176 60 116
Cusp forms 160 60 100
Eisenstein series 16 0 16

Trace form

\( 60 q - 2 q^{2} + 6 q^{4} - 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 60 q - 2 q^{2} + 6 q^{4} - 4 q^{7} + 4 q^{8} + 6 q^{10} + 6 q^{14} + 2 q^{16} - 20 q^{20} - 4 q^{22} + 8 q^{23} - 60 q^{25} + 8 q^{28} + 28 q^{31} + 8 q^{32} - 28 q^{34} + 4 q^{38} - 34 q^{40} + 8 q^{41} - 20 q^{44} - 4 q^{46} - 44 q^{47} + 60 q^{49} + 26 q^{50} - 4 q^{52} - 16 q^{55} + 46 q^{56} - 16 q^{58} - 18 q^{64} - 6 q^{68} + 24 q^{70} + 20 q^{71} + 70 q^{74} + 28 q^{76} - 24 q^{79} + 4 q^{80} + 36 q^{82} - 52 q^{86} + 40 q^{88} - 16 q^{89} - 24 q^{92} - 14 q^{94} + 24 q^{95} - 16 q^{97} + 14 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(936, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
936.2.g.a 936.g 8.b $2$ $7.474$ \(\Q(\sqrt{-1}) \) None 104.2.b.a \(2\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i+1)q^{2}+2 i q^{4}+3 i q^{5}+3 q^{7}+\cdots\)
936.2.g.b 936.g 8.b $4$ $7.474$ \(\Q(\zeta_{12})\) None 104.2.b.b \(-2\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta_{2}-\beta_1)q^{2}+(\beta_{3}+\beta_1)q^{4}+(-2\beta_{3}+2\beta_1-2)q^{5}+\cdots\)
936.2.g.c 936.g 8.b $6$ $7.474$ 6.0.399424.1 None 104.2.b.c \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{5})q^{4}-\beta _{1}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
936.2.g.d 936.g 8.b $8$ $7.474$ \(\Q(\zeta_{20})\) None 312.2.g.a \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_{6} q^{2}-\beta_1 q^{4}+(\beta_{6}-\beta_{5}-\beta_{3}+\cdots+1)q^{5}+\cdots\)
936.2.g.e 936.g 8.b $16$ $7.474$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 312.2.g.b \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}-\beta _{2}q^{4}-\beta _{14}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
936.2.g.f 936.g 8.b $24$ $7.474$ None 936.2.g.f \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(936, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)