Properties

Label 912.2.d
Level $912$
Weight $2$
Character orbit 912.d
Rep. character $\chi_{912}(191,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $320$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(320\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 172 36 136
Cusp forms 148 36 112
Eisenstein series 24 0 24

Trace form

\( 36q + O(q^{10}) \) \( 36q - 24q^{21} - 60q^{25} + 48q^{37} - 12q^{49} - 48q^{61} + 24q^{73} + 24q^{81} - 48q^{85} + 72q^{93} - 24q^{97} + O(q^{100}) \)

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.d.a \(12\) \(7.282\) 12.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.d.b \(24\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)