Properties

Label 1520.2.bn
Level $1520$
Weight $2$
Character orbit 1520.bn
Rep. character $\chi_{1520}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $472$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.bn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1520 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472q + 8q^{4} - 4q^{5} - 8q^{6} + 456q^{9} + O(q^{10}) \) \( 472q + 8q^{4} - 4q^{5} - 8q^{6} + 456q^{9} - 8q^{11} - 16q^{16} - 8q^{17} + 8q^{19} + 8q^{20} - 24q^{24} - 24q^{26} - 32q^{28} - 16q^{30} - 8q^{35} - 8q^{36} - 32q^{38} - 48q^{39} - 8q^{43} + 16q^{44} - 36q^{45} - 8q^{47} - 56q^{54} - 12q^{57} + 24q^{58} - 40q^{61} + 24q^{62} - 64q^{63} + 32q^{64} + 56q^{66} + 40q^{68} - 48q^{74} - 36q^{76} + 48q^{77} - 16q^{80} + 392q^{81} + 88q^{82} + 16q^{85} - 24q^{87} - 80q^{92} + 20q^{95} + 80q^{96} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.