↑

Properties

Label 936.2.w
Level $936$
Weight $2$
Character orbit 936.w
Rep. character $\chi_{936}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $136$
Newform subspaces $11$
Sturm bound $336$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 11 \)
Sturm bound: \(336\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 352 144 208
Cusp forms 320 136 184
Eisenstein series 32 8 24

Trace form

\( 136 q + 2 q^{2} - 4 q^{8} + O(q^{10}) \) \( 136 q + 2 q^{2} - 4 q^{8} + 4 q^{11} - 12 q^{14} - 12 q^{16} - 4 q^{19} + 28 q^{20} - 32 q^{22} + 14 q^{26} - 12 q^{28} + 12 q^{32} - 8 q^{34} + 8 q^{35} - 52 q^{40} + 8 q^{41} - 4 q^{44} - 52 q^{46} + 42 q^{50} + 36 q^{52} + 28 q^{58} + 12 q^{59} - 4 q^{67} + 28 q^{68} - 28 q^{70} + 32 q^{73} - 64 q^{74} + 36 q^{76} + 16 q^{80} + 44 q^{83} - 16 q^{86} - 16 q^{89} + 76 q^{91} - 8 q^{92} - 76 q^{94} + 16 q^{97} - 110 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.w.a 936.w 104.m $2$ $7.474$ \(\Q(\sqrt{-1}) \) None 312.2.t.a \(-2\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{2}-2 i q^{4}+(2 i-2)q^{5}+\cdots\)
936.2.w.b 936.w 104.m $2$ $7.474$ \(\Q(\sqrt{-1}) \) None 312.2.t.b \(2\) \(0\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i+1)q^{2}+2 i q^{4}+(2 i-2)q^{5}+\cdots\)
936.2.w.c 936.w 104.m $2$ $7.474$ \(\Q(\sqrt{-1}) \) None 312.2.t.b \(2\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i+1)q^{2}+2 i q^{4}+(-2 i+2)q^{5}+\cdots\)
936.2.w.d 936.w 104.m $2$ $7.474$ \(\Q(\sqrt{-1}) \) None 312.2.t.a \(2\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i+1)q^{2}-2 i q^{4}+(-2 i+2)q^{5}+\cdots\)
936.2.w.e 936.w 104.m $4$ $7.474$ \(\Q(\zeta_{8})\) None 936.2.w.e \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta_{2} q^{2}-2 q^{4}+(2\beta_{3}+2\beta_{2})q^{5}+\cdots\)
936.2.w.f 936.w 104.m $4$ $7.474$ \(\Q(\zeta_{8})\) None 936.2.w.e \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta_{3} q^{2}+2 q^{4}+(2\beta_{3}+2\beta_{2})q^{5}+\cdots\)
936.2.w.g 936.w 104.m $4$ $7.474$ \(\Q(i, \sqrt{26})\) None 104.2.m.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+\cdots\)
936.2.w.h 936.w 104.m $20$ $7.474$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 104.2.m.b \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{11}q^{2}-\beta _{13}q^{4}+(-\beta _{3}+\beta _{11}+\cdots)q^{5}+\cdots\)
936.2.w.i 936.w 104.m $24$ $7.474$ None 312.2.t.f \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
936.2.w.j 936.w 104.m $24$ $7.474$ None 312.2.t.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
936.2.w.k 936.w 104.m $48$ $7.474$ None 936.2.w.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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