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Properties

Label 936.2.t
Level $936$
Weight $2$
Character orbit 936.t
Rep. character $\chi_{936}(217,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $34$
Newform subspaces $9$
Sturm bound $336$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
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 368 34 334
Cusp forms 304 34 270
Eisenstein series 64 0 64

Trace form

\( 34 q - 2 q^{5} - 2 q^{7} + O(q^{10}) \) \( 34 q - 2 q^{5} - 2 q^{7} - 2 q^{11} + q^{13} - q^{17} + 2 q^{19} + 2 q^{23} + 28 q^{25} - 5 q^{29} - 24 q^{31} + 4 q^{35} + 5 q^{37} - 13 q^{41} + 2 q^{43} + 16 q^{47} - 7 q^{49} + 22 q^{53} - 8 q^{55} + 10 q^{59} - 3 q^{61} + 17 q^{65} - 26 q^{67} - 6 q^{71} + 34 q^{73} + 60 q^{77} + 16 q^{79} + 48 q^{83} + 9 q^{85} + 20 q^{89} - 30 q^{91} - 16 q^{95} + 8 q^{97} + O(q^{100}) \)

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.t.a 936.t 13.c $2$ $7.474$ \(\Q(\sqrt{-3}) \) None 312.2.q.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-3q^{5}+(3+\zeta_{6})q^{13}-\zeta_{6}q^{17}+(4+\cdots)q^{23}+\cdots\)
936.2.t.b 936.t 13.c $2$ $7.474$ \(\Q(\sqrt{-3}) \) None 312.2.q.c \(0\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-3q^{5}+4\zeta_{6}q^{7}+(4-4\zeta_{6})q^{11}+(-1+\cdots)q^{13}+\cdots\)
936.2.t.c 936.t 13.c $2$ $7.474$ \(\Q(\sqrt{-3}) \) None 104.2.i.a \(0\) \(0\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-2q^{5}+\zeta_{6}q^{7}+(1-\zeta_{6})q^{11}+(1-4\zeta_{6})q^{13}+\cdots\)
936.2.t.d 936.t 13.c $2$ $7.474$ \(\Q(\sqrt{-3}) \) None 312.2.q.b \(0\) \(0\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2q^{5}-\zeta_{6}q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
936.2.t.e 936.t 13.c $4$ $7.474$ \(\Q(\sqrt{-3}, \sqrt{13})\) None 312.2.q.d \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
936.2.t.f 936.t 13.c $4$ $7.474$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 104.2.i.b \(0\) \(0\) \(6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{1}q^{11}+\cdots\)
936.2.t.g 936.t 13.c $6$ $7.474$ 6.0.27870912.1 None 936.2.t.g \(0\) \(0\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}-\beta _{5}q^{11}+\cdots\)
936.2.t.h 936.t 13.c $6$ $7.474$ 6.0.2101707.2 None 312.2.q.e \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{5}+(-2-\beta _{4}+2\beta _{5})q^{7}+(-2+\cdots)q^{11}+\cdots\)
936.2.t.i 936.t 13.c $6$ $7.474$ 6.0.27870912.1 None 936.2.t.g \(0\) \(0\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{3}-\beta _{5})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)