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Properties

Label 1530.2.cq
Level $1530$
Weight $2$
Character orbit 1530.cq
Rep. character $\chi_{1530}(11,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1152$
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.cq (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 5312 1152 4160
Cusp forms 5056 1152 3904
Eisenstein series 256 0 256

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 32 q^{12} - 64 q^{18} - 16 q^{24} + 48 q^{38} + 32 q^{39} + 48 q^{43} + 64 q^{45} + 128 q^{51} + 16 q^{54} - 16 q^{57} + 32 q^{60} + 96 q^{63} + 96 q^{65} + 16 q^{66} + 128 q^{69} - 16 q^{81} + 96 q^{87} - 192 q^{91} + 128 q^{93} + 208 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)