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Properties

Label 1428.2.m
Level $1428$
Weight $2$
Character orbit 1428.m
Rep. character $\chi_{1428}(407,\cdot)$
Character field $\Q$
Dimension $216$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1428.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 204 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

Total New Old
Modular forms 296 216 80
Cusp forms 280 216 64
Eisenstein series 16 0 16

Trace form

\( 216 q + 8 q^{4} - 8 q^{9} + O(q^{10}) \) \( 216 q + 8 q^{4} - 8 q^{9} + 8 q^{16} + 216 q^{25} - 10 q^{30} + 48 q^{33} + 24 q^{34} + 10 q^{36} - 10 q^{42} + 216 q^{49} - 32 q^{52} - 122 q^{60} + 56 q^{64} + 8 q^{66} - 10 q^{72} + 16 q^{76} + 40 q^{81} - 28 q^{84} - 56 q^{85} - 56 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)