Properties

Label 760.2.f
Level $760$
Weight $2$
Character orbit 760.f
Rep. character $\chi_{760}(381,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 124 72 52
Cusp forms 116 72 44
Eisenstein series 8 0 8

Trace form

\( 72q + 4q^{2} - 4q^{4} - 12q^{6} + 8q^{7} + 16q^{8} - 72q^{9} + O(q^{10}) \) \( 72q + 4q^{2} - 4q^{4} - 12q^{6} + 8q^{7} + 16q^{8} - 72q^{9} + 8q^{12} + 8q^{14} - 12q^{16} - 28q^{18} - 8q^{20} - 8q^{22} + 8q^{23} - 4q^{24} - 72q^{25} + 12q^{26} - 4q^{28} + 8q^{30} - 16q^{32} + 32q^{34} + 16q^{36} - 48q^{39} + 4q^{42} + 24q^{46} - 40q^{47} + 12q^{48} + 72q^{49} - 4q^{50} + 12q^{52} + 36q^{54} + 16q^{55} + 32q^{56} - 52q^{58} - 28q^{60} - 24q^{62} + 40q^{63} - 4q^{64} + 72q^{66} - 44q^{68} - 8q^{70} - 16q^{71} - 4q^{72} + 40q^{74} - 88q^{78} + 80q^{79} - 8q^{80} + 88q^{81} + 24q^{82} - 56q^{84} - 88q^{86} + 96q^{87} + 60q^{88} - 16q^{89} - 12q^{92} - 16q^{95} + 84q^{96} - 4q^{98} + O(q^{100}) \)

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.f.a \(28\) \(6.069\) None \(2\) \(0\) \(0\) \(4\)
760.2.f.b \(44\) \(6.069\) None \(2\) \(0\) \(0\) \(4\)

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

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)