Properties

Label 912.2.ch
Level $912$
Weight $2$
Character orbit 912.ch
Rep. character $\chi_{912}(47,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
Newform subspaces $7$
Sturm bound $320$
Trace bound $19$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.ch (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 7 \)
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 240 792
Cusp forms 888 240 648
Eisenstein series 144 0 144

Trace form

\( 240q + 18q^{9} + O(q^{10}) \) \( 240q + 18q^{9} + 12q^{13} - 18q^{33} + 120q^{49} + 24q^{61} + 228q^{73} - 18q^{81} + 72q^{85} + 108q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
912.2.ch.a \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\zeta_{18}-\zeta_{18}^{4})q^{3}+(3\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.ch.b \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-2\zeta_{18}+\zeta_{18}^{4})q^{3}+(-3\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.ch.c \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-2\zeta_{18}+\zeta_{18}^{4})q^{3}+(\zeta_{18}+3\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.ch.d \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\zeta_{18}-\zeta_{18}^{4})q^{3}+(-\zeta_{18}-3\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.ch.e \(72\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)
912.2.ch.f \(72\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)
912.2.ch.g \(72\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)

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

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