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Properties

Label 912.2.q
Level $912$
Weight $2$
Character orbit 912.q
Rep. character $\chi_{912}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $12$
Sturm bound $320$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(320\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 344 40 304
Cusp forms 296 40 256
Eisenstein series 48 0 48

Trace form

\( 40 q - 2 q^{3} - 4 q^{7} - 20 q^{9} + O(q^{10}) \) \( 40 q - 2 q^{3} - 4 q^{7} - 20 q^{9} + 4 q^{15} + 8 q^{19} - 12 q^{23} - 20 q^{25} + 4 q^{27} - 20 q^{31} + 12 q^{35} - 4 q^{39} - 8 q^{41} + 2 q^{43} - 12 q^{47} + 48 q^{49} - 16 q^{51} - 8 q^{53} - 4 q^{57} - 24 q^{61} + 2 q^{63} - 32 q^{65} + 26 q^{67} + 32 q^{69} + 12 q^{71} + 4 q^{73} + 28 q^{75} + 16 q^{77} + 42 q^{79} - 20 q^{81} + 112 q^{83} + 48 q^{87} - 16 q^{89} - 50 q^{91} + 16 q^{93} - 52 q^{95} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.2.q.a 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots\)
912.2.q.b 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots\)
912.2.q.c 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+5q^{7}+\cdots\)
912.2.q.d 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+3q^{7}+\cdots\)
912.2.q.e 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+3q^{7}+\cdots\)
912.2.q.f 912.q 19.c $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3q^{7}-\zeta_{6}q^{9}-2q^{11}+\cdots\)
912.2.q.g 912.q 19.c $4$ $7.282$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(-2\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
912.2.q.h 912.q 19.c $4$ $7.282$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
912.2.q.i 912.q 19.c $4$ $7.282$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
912.2.q.j 912.q 19.c $4$ $7.282$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(2\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
912.2.q.k 912.q 19.c $6$ $7.282$ \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{18}^{2}q^{3}+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
912.2.q.l 912.q 19.c $6$ $7.282$ 6.0.954288.1 None \(0\) \(3\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)