Properties

Label 276.2.c
Level $276$
Weight $2$
Character orbit 276.c
Rep. character $\chi_{276}(47,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $2$
Sturm bound $96$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 52 44 8
Cusp forms 44 44 0
Eisenstein series 8 0 8

Trace form

\( 44q - 3q^{6} - 4q^{9} + O(q^{10}) \) \( 44q - 3q^{6} - 4q^{9} + 8q^{10} + 7q^{12} - 8q^{13} + 8q^{16} - q^{18} + 4q^{22} - 8q^{24} - 36q^{25} + 12q^{28} + 10q^{30} - 16q^{33} - 12q^{34} - 33q^{36} - 8q^{37} - 8q^{40} - 12q^{42} - 5q^{48} - 28q^{49} - 38q^{52} - 32q^{54} + 24q^{57} + 6q^{58} + 36q^{60} + 24q^{61} + 6q^{64} + 42q^{66} + 12q^{72} - 8q^{73} + 52q^{76} - 35q^{78} + 20q^{81} - 58q^{82} + 38q^{84} + 16q^{85} - 60q^{88} + 58q^{90} + 24q^{93} - 26q^{94} - 27q^{96} - 8q^{97} + O(q^{100}) \)

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.c.a \(22\) \(2.204\) None \(0\) \(0\) \(0\) \(0\)
276.2.c.b \(22\) \(2.204\) None \(0\) \(0\) \(0\) \(0\)