Properties

Label 276.2.o
Level $276$
Weight $2$
Character orbit 276.o
Rep. character $\chi_{276}(35,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $440$
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.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 276 \)
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 520 520 0
Cusp forms 440 440 0
Eisenstein series 80 80 0

Trace form

\( 440q - 22q^{4} - 8q^{6} - 18q^{9} + O(q^{10}) \) \( 440q - 22q^{4} - 8q^{6} - 18q^{9} - 30q^{10} - 18q^{12} - 36q^{13} - 30q^{16} - 10q^{18} - 22q^{21} - 48q^{22} - 14q^{24} - 8q^{25} - 34q^{28} - 21q^{30} - 6q^{33} - 32q^{34} + 22q^{36} - 36q^{37} - 168q^{40} + q^{42} - 44q^{45} - 110q^{46} - 6q^{48} - 16q^{49} - 94q^{52} + 21q^{54} - 46q^{57} - 116q^{58} - 47q^{60} - 68q^{61} - 28q^{64} - 20q^{66} - 22q^{69} - 44q^{70} - 23q^{72} - 36q^{73} - 74q^{76} + 134q^{78} - 130q^{81} + 36q^{82} + 105q^{84} - 60q^{85} + 38q^{88} + 162q^{90} - 332q^{93} - 40q^{94} + 225q^{96} - 36q^{97} + O(q^{100}) \)

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.o.a \(440\) \(2.204\) None \(0\) \(0\) \(0\) \(0\)