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Properties

Label 1428.2.cs
Level $1428$
Weight $2$
Character orbit 1428.cs
Rep. character $\chi_{1428}(19,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1152$
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.cs (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2368 1152 1216
Cusp forms 2240 1152 1088
Eisenstein series 128 0 128

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 64 q^{14} + 48 q^{22} + 24 q^{28} - 40 q^{32} + 24 q^{42} + 32 q^{44} - 72 q^{56} + 96 q^{61} - 384 q^{68} + 24 q^{70} - 128 q^{77} - 48 q^{78} - 264 q^{82} + 48 q^{84} + 64 q^{86} + 88 q^{88} - 32 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)