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Properties

Label 1428.2.bj
Level $1428$
Weight $2$
Character orbit 1428.bj
Rep. character $\chi_{1428}(443,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $512$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 512 80
Cusp forms 560 512 48
Eisenstein series 32 0 32

Trace form

\( 512 q + O(q^{10}) \) \( 512 q + 16 q^{13} + 16 q^{16} - 8 q^{21} - 32 q^{22} + 264 q^{25} + 10 q^{30} - 60 q^{36} + 8 q^{37} - 20 q^{40} - 64 q^{42} - 8 q^{45} - 36 q^{46} - 36 q^{48} - 16 q^{49} - 40 q^{52} - 72 q^{54} - 32 q^{57} - 40 q^{58} - 38 q^{60} - 16 q^{61} + 72 q^{64} - 76 q^{66} - 48 q^{69} + 88 q^{70} + 12 q^{72} - 8 q^{73} - 48 q^{76} + 116 q^{78} - 56 q^{81} + 116 q^{82} + 126 q^{84} + 8 q^{88} + 80 q^{90} - 8 q^{93} + 12 q^{94} + 100 q^{96} - 176 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)