Properties

Label 1476.2.s
Level $1476$
Weight $2$
Character orbit 1476.s
Rep. character $\chi_{1476}(491,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $496$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1476 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 512 512 0
Cusp forms 496 496 0
Eisenstein series 16 16 0

Trace form

\( 496 q - 6 q^{2} - 2 q^{4} - 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 496 q - 6 q^{2} - 2 q^{4} - 12 q^{5} - 12 q^{9} - 16 q^{10} - 2 q^{16} - 14 q^{18} - 6 q^{20} - 4 q^{21} + 228 q^{25} - 66 q^{32} + 16 q^{33} + 70 q^{36} - 16 q^{37} + 8 q^{40} - 36 q^{41} - 62 q^{42} - 44 q^{45} - 228 q^{49} - 36 q^{50} - 4 q^{57} - 4 q^{61} + 28 q^{64} - 62 q^{66} - 20 q^{72} - 40 q^{73} + 24 q^{74} - 12 q^{77} - 12 q^{78} - 28 q^{81} - 26 q^{82} + 48 q^{84} + 54 q^{86} - 130 q^{90} - 60 q^{92} + O(q^{100}) \)

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

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