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Properties

Label 1428.2.by
Level $1428$
Weight $2$
Character orbit 1428.by
Rep. character $\chi_{1428}(115,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
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.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1184 576 608
Cusp forms 1120 576 544
Eisenstein series 64 0 64

Trace form

\( 576 q + O(q^{10}) \) \( 576 q - 32 q^{14} - 24 q^{22} - 36 q^{24} + 32 q^{30} + 16 q^{44} - 20 q^{46} + 72 q^{52} + 108 q^{56} - 12 q^{58} + 48 q^{61} - 48 q^{64} - 72 q^{68} + 44 q^{74} + 24 q^{78} + 288 q^{81} + 12 q^{82} - 24 q^{84} + 32 q^{85} + 24 q^{86} - 68 q^{88} + 152 q^{98} + O(q^{100}) \)

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

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