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Properties

Label 1428.2.bk
Level $1428$
Weight $2$
Character orbit 1428.bk
Rep. character $\chi_{1428}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 592 256 336
Cusp forms 560 256 304
Eisenstein series 32 0 32

Trace form

\( 256 q - 4 q^{2} + 4 q^{4} - 16 q^{8} - 128 q^{9} + O(q^{10}) \) \( 256 q - 4 q^{2} + 4 q^{4} - 16 q^{8} - 128 q^{9} + 36 q^{10} + 12 q^{14} + 4 q^{16} - 4 q^{18} + 16 q^{21} + 136 q^{25} + 12 q^{28} + 64 q^{29} - 4 q^{32} + 24 q^{33} - 8 q^{36} - 24 q^{37} - 36 q^{38} + 60 q^{40} - 20 q^{42} + 24 q^{44} - 4 q^{46} - 16 q^{49} - 8 q^{50} - 108 q^{52} + 32 q^{53} - 36 q^{56} - 48 q^{57} - 16 q^{58} + 44 q^{60} - 8 q^{64} - 16 q^{65} + 36 q^{66} + 20 q^{70} + 8 q^{72} + 72 q^{73} + 32 q^{74} + 48 q^{78} + 144 q^{80} - 128 q^{81} + 60 q^{82} + 12 q^{84} - 32 q^{86} + 32 q^{88} + 112 q^{92} - 8 q^{93} + 72 q^{94} - 60 q^{96} + 80 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)