Properties

Label 760.2.cc
Level $760$
Weight $2$
Character orbit 760.cc
Rep. character $\chi_{760}(61,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.cc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

Total New Old
Modular forms 744 480 264
Cusp forms 696 480 216
Eisenstein series 48 0 48

Trace form

\( 480q + 6q^{4} + 6q^{6} + O(q^{10}) \) \( 480q + 6q^{4} + 6q^{6} - 6q^{10} - 6q^{16} - 24q^{26} + 24q^{30} - 60q^{32} + 84q^{34} - 144q^{36} - 30q^{38} + 24q^{41} + 186q^{42} - 126q^{44} + 30q^{46} + 114q^{48} - 240q^{49} - 18q^{52} - 90q^{54} - 12q^{60} + 72q^{62} + 12q^{64} - 156q^{66} - 78q^{68} - 72q^{70} - 84q^{72} - 48q^{73} - 132q^{74} - 132q^{76} - 60q^{78} - 48q^{80} - 24q^{81} + 30q^{82} - 36q^{84} - 30q^{86} - 48q^{88} - 102q^{90} + 84q^{92} - 24q^{94} - 156q^{96} - 144q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
760.2.cc.a \(480\) \(6.069\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)