Properties

Label 912.2.u
Level $912$
Weight $2$
Character orbit 912.u
Rep. character $\chi_{912}(229,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Newform subspaces $2$
Sturm bound $320$
Trace bound $20$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(320\)
Trace bound: \(20\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 328 144 184
Cusp forms 312 144 168
Eisenstein series 16 0 16

Trace form

\( 144q + 8q^{4} + O(q^{10}) \) \( 144q + 8q^{4} + 16q^{11} - 16q^{12} - 24q^{14} - 8q^{16} - 8q^{18} - 32q^{20} + 24q^{28} + 32q^{29} + 16q^{30} + 32q^{34} + 32q^{37} + 8q^{40} + 40q^{42} + 16q^{43} + 24q^{44} + 32q^{48} - 144q^{49} + 56q^{50} + 64q^{52} - 32q^{53} - 56q^{56} - 24q^{58} - 64q^{59} + 48q^{62} - 16q^{63} + 56q^{64} + 32q^{65} - 16q^{67} - 24q^{68} - 40q^{70} + 8q^{72} - 144q^{74} - 32q^{75} - 32q^{77} - 24q^{78} + 88q^{80} - 144q^{81} - 40q^{82} + 48q^{84} + 96q^{86} - 64q^{88} + 16q^{90} + 16q^{91} + 8q^{92} + 24q^{94} - 40q^{96} + 160q^{98} + 16q^{99} + O(q^{100}) \)

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.u.a \(72\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)
912.2.u.b \(72\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)