Properties

Label 1530.2.bv
Level $1530$
Weight $2$
Character orbit 1530.bv
Rep. character $\chi_{1530}(353,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1530.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 765 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1530, [\chi])\).

Total New Old
Modular forms 1328 432 896
Cusp forms 1264 432 832
Eisenstein series 64 0 64

Trace form

\( 432 q + 32 q^{9} + O(q^{10}) \) \( 432 q + 32 q^{9} + 24 q^{11} + 216 q^{16} - 8 q^{39} - 48 q^{41} - 28 q^{45} + 120 q^{47} + 216 q^{49} + 64 q^{51} - 24 q^{54} + 84 q^{65} - 36 q^{68} - 4 q^{75} + 24 q^{79} + 32 q^{81} - 96 q^{82} - 24 q^{85} + 104 q^{87} - 56 q^{90} + 48 q^{91} + 96 q^{93} + 24 q^{95} + 48 q^{97} - 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1530, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1530, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)