Properties

Label 276.2.m
Level $276$
Weight $2$
Character orbit 276.m
Rep. character $\chi_{276}(7,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.m (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(276, [\chi])\).

Total New Old
Modular forms 520 240 280
Cusp forms 440 240 200
Eisenstein series 80 0 80

Trace form

\( 240q - 4q^{2} - 4q^{6} - 4q^{8} + 24q^{9} + O(q^{10}) \) \( 240q - 4q^{2} - 4q^{6} - 4q^{8} + 24q^{9} - 8q^{16} + 4q^{18} + 4q^{24} + 24q^{25} - 40q^{26} + 32q^{29} + 36q^{32} - 22q^{34} - 22q^{36} - 110q^{38} - 22q^{40} - 16q^{41} - 110q^{42} - 154q^{44} - 88q^{46} - 56q^{48} - 40q^{49} - 142q^{50} - 70q^{52} - 18q^{54} - 110q^{56} - 46q^{58} - 22q^{60} + 40q^{62} - 48q^{64} - 16q^{69} - 72q^{70} + 4q^{72} + 22q^{74} + 110q^{76} - 192q^{77} + 198q^{80} - 24q^{81} + 172q^{82} - 200q^{85} + 220q^{86} + 176q^{88} - 88q^{89} + 154q^{92} - 16q^{93} + 126q^{94} - 44q^{96} - 88q^{97} + 228q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(276, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
276.2.m.a \(240\) \(2.204\) None \(-4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(276, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(276, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)