Properties

Label 912.2.bb
Level $912$
Weight $2$
Character orbit 912.bb
Rep. character $\chi_{912}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $8$
Sturm bound $320$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(23\), \(31\)

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

\( 40q - 20q^{9} + O(q^{10}) \) \( 40q - 20q^{9} - 12q^{13} - 12q^{21} - 20q^{25} - 72q^{41} - 80q^{49} + 72q^{53} - 4q^{57} + 28q^{61} + 4q^{73} + 96q^{77} - 20q^{81} - 48q^{85} + 144q^{89} - 44q^{93} + 72q^{97} + O(q^{100}) \)

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.bb.a \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
912.2.bb.b \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
912.2.bb.c \(4\) \(7.282\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1+\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
912.2.bb.d \(4\) \(7.282\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(0\) \(q+(1-\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots\)
912.2.bb.e \(6\) \(7.282\) 6.0.954288.1 None \(0\) \(-3\) \(-2\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bb.f \(6\) \(7.282\) 6.0.954288.1 None \(0\) \(3\) \(-2\) \(0\) \(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bb.g \(8\) \(7.282\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(-2\) \(0\) \(q+(-1-\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
912.2.bb.h \(8\) \(7.282\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(-2\) \(0\) \(q+(1+\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots\)

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

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