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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

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

Display 100 coefficients 10 coefficients

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

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