Properties

Label 912.2.ci
Level $912$
Weight $2$
Character orbit 912.ci
Rep. character $\chi_{912}(79,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $8$
Sturm bound $320$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.ci (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 1032 120 912
Cusp forms 888 120 768
Eisenstein series 144 0 144

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 12 q^{13} + 12 q^{21} + 72 q^{41} + 60 q^{49} - 72 q^{53} - 48 q^{61} + 216 q^{65} - 12 q^{73} + 144 q^{77} + 72 q^{85} + 72 q^{89} + 24 q^{93} - 72 q^{97} + O(q^{100}) \)

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.ci.a 912.ci 76.k $6$ $7.282$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-6\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q+\zeta_{18}^{2}q^{3}+(-1-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.ci.b 912.ci 76.k $6$ $7.282$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-6\) \(9\) $\mathrm{SU}(2)[C_{18}]$ \(q-\zeta_{18}^{2}q^{3}+(-1-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.ci.c 912.ci 76.k $12$ $7.282$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(-18\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{8}q^{3}+(1+\beta _{1}+\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
912.2.ci.d 912.ci 76.k $12$ $7.282$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(18\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{8}q^{3}+(1+\beta _{1}+\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
912.2.ci.e 912.ci 76.k $18$ $7.282$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)
912.2.ci.f 912.ci 76.k $18$ $7.282$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)
912.2.ci.g 912.ci 76.k $24$ $7.282$ None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$
912.2.ci.h 912.ci 76.k $24$ $7.282$ None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)