Properties

Label 912.2.cc
Level $912$
Weight $2$
Character orbit 912.cc
Rep. character $\chi_{912}(257,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $228$
Newform subspaces $8$
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.cc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(13\)
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 252 780
Cusp forms 888 228 660
Eisenstein series 144 24 120

Trace form

\( 228q + 6q^{3} + 6q^{7} - 12q^{9} + O(q^{10}) \) \( 228q + 6q^{3} + 6q^{7} - 12q^{9} - 12q^{13} + 6q^{15} + 6q^{19} + 3q^{21} - 12q^{25} + 9q^{27} + 18q^{31} - 9q^{33} + 12q^{39} + 54q^{43} - 3q^{45} - 84q^{49} + 6q^{51} + 6q^{55} - 6q^{57} - 12q^{61} - 69q^{63} + 90q^{67} - 9q^{69} - 72q^{73} + 96q^{79} + 60q^{85} + 3q^{87} + 54q^{91} - 15q^{93} + 24q^{97} + 33q^{99} + O(q^{100}) \)

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.cc.a \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{18}^{2}-2\zeta_{18}^{5})q^{3}+(3\zeta_{18}-2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.cc.b \(6\) \(7.282\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+(\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.cc.c \(18\) \(7.282\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) \(q+\beta _{12}q^{3}+(-\beta _{2}-\beta _{14}+\beta _{15})q^{5}+\cdots\)
912.2.cc.d \(18\) \(7.282\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{3}+(-\beta _{9}+\beta _{17})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.cc.e \(24\) \(7.282\) None \(0\) \(9\) \(0\) \(6\)
912.2.cc.f \(36\) \(7.282\) None \(0\) \(-3\) \(0\) \(0\)
912.2.cc.g \(60\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)
912.2.cc.h \(60\) \(7.282\) None \(0\) \(3\) \(0\) \(0\)

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

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