Properties

Label 76.2.f
Level $76$
Weight $2$
Character orbit 76.f
Rep. character $\chi_{76}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
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 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16q - 3q^{2} - 3q^{4} - 2q^{5} + 5q^{6} - 4q^{9} + O(q^{10}) \) \( 16q - 3q^{2} - 3q^{4} - 2q^{5} + 5q^{6} - 4q^{9} - 6q^{10} - 18q^{13} - 6q^{14} - 3q^{16} + 2q^{17} + 4q^{20} + 3q^{22} - 23q^{24} - 2q^{25} - 24q^{26} - 4q^{28} - 6q^{29} + 28q^{30} + 27q^{32} + 18q^{33} + 36q^{34} + 14q^{36} - 24q^{38} + 48q^{40} - 48q^{41} + 28q^{42} - 25q^{44} + 24q^{45} + 9q^{48} + 16q^{49} + 6q^{52} + 6q^{53} + 17q^{54} - 26q^{57} - 40q^{58} - 6q^{60} - 26q^{61} + 32q^{62} - 18q^{64} + 5q^{66} - 36q^{68} - 54q^{70} - 66q^{72} + 16q^{73} - 2q^{74} + 43q^{76} + 80q^{77} - 84q^{78} - 30q^{80} + 12q^{81} + 11q^{82} + 14q^{85} - 48q^{86} + 18q^{89} - 18q^{90} - 52q^{92} - 20q^{93} + 46q^{96} - 12q^{97} + 51q^{98} + O(q^{100}) \)

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.f.a \(16\) \(0.607\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(0\) \(-2\) \(0\) \(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)