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Properties

Label 1476.2.ck
Level $1476$
Weight $2$
Character orbit 1476.ck
Rep. character $\chi_{1476}(29,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $1344$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.ck (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 369 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

Total New Old
Modular forms 8256 1344 6912
Cusp forms 7872 1344 6528
Eisenstein series 384 0 384

Trace form

\( 1344 q + 4 q^{3} + 12 q^{9} + O(q^{10}) \) \( 1344 q + 4 q^{3} + 12 q^{9} + 12 q^{15} - 20 q^{21} - 32 q^{27} + 56 q^{33} - 64 q^{39} - 80 q^{45} - 24 q^{49} + 64 q^{51} - 16 q^{57} + 68 q^{63} - 84 q^{65} - 48 q^{67} + 44 q^{69} + 16 q^{75} + 240 q^{83} + 192 q^{85} - 28 q^{87} - 56 q^{93} - 96 q^{95} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(369, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(738, [\chi])\)\(^{\oplus 2}\)