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Properties

Label 1530.2.ba
Level $1530$
Weight $2$
Character orbit 1530.ba
Rep. character $\chi_{1530}(781,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 664 144 520
Cusp forms 632 144 488
Eisenstein series 32 0 32

Trace form

\( 144 q - 4 q^{2} - 72 q^{4} + 8 q^{8} + 20 q^{9} + O(q^{10}) \) \( 144 q - 4 q^{2} - 72 q^{4} + 8 q^{8} + 20 q^{9} + 8 q^{15} - 72 q^{16} - 4 q^{17} + 16 q^{18} - 24 q^{19} - 48 q^{21} + 72 q^{25} - 16 q^{26} - 4 q^{32} - 28 q^{33} - 6 q^{34} - 16 q^{35} - 4 q^{36} + 20 q^{38} - 32 q^{42} - 12 q^{43} + 24 q^{47} + 72 q^{49} + 4 q^{50} + 58 q^{51} + 96 q^{53} + 28 q^{59} + 8 q^{60} + 144 q^{64} + 16 q^{66} + 12 q^{67} + 2 q^{68} - 72 q^{69} + 4 q^{72} + 12 q^{76} - 48 q^{77} - 116 q^{81} + 12 q^{85} - 28 q^{86} + 32 q^{87} + 64 q^{89} + 48 q^{93} - 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)