Properties

Label 76.2.d
Level $76$
Weight $2$
Character orbit 76.d
Rep. character $\chi_{76}(75,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(76, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} + O(q^{10}) \) \( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} - 6q^{16} - 8q^{17} + 20q^{20} - 10q^{24} - 4q^{25} - 6q^{26} + 22q^{28} - 16q^{30} - 20q^{36} + 18q^{38} + 50q^{42} + 16q^{44} - 36q^{45} - 16q^{49} + 22q^{54} + 20q^{57} - 38q^{58} + 44q^{61} - 20q^{62} - 18q^{64} - 44q^{66} + 6q^{68} + 32q^{73} + 44q^{74} - 16q^{76} + 28q^{77} - 48q^{80} - 48q^{81} - 44q^{82} + 4q^{85} - 38q^{92} + 8q^{93} + 74q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.2.d.a \(8\) \(0.607\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)