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Properties

Label 1428.2.h
Level $1428$
Weight $2$
Character orbit 1428.h
Rep. character $\chi_{1428}(239,\cdot)$
Character field $\Q$
Dimension $192$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
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 296 192 104
Cusp forms 280 192 88
Eisenstein series 16 0 16

Trace form

\( 192 q + 12 q^{6} + O(q^{10}) \) \( 192 q + 12 q^{6} - 16 q^{10} + 12 q^{12} + 16 q^{18} + 32 q^{22} - 4 q^{24} - 192 q^{25} - 16 q^{28} - 50 q^{30} + 30 q^{36} + 16 q^{40} - 10 q^{42} - 48 q^{45} - 16 q^{46} - 40 q^{48} - 192 q^{49} + 88 q^{52} + 32 q^{54} + 16 q^{57} + 32 q^{58} - 38 q^{60} - 96 q^{64} + 32 q^{66} + 48 q^{69} + 24 q^{70} - 10 q^{72} + 40 q^{76} - 12 q^{78} - 16 q^{81} - 16 q^{82} + 80 q^{88} - 28 q^{90} - 48 q^{93} + 40 q^{94} + 44 q^{96} + O(q^{100}) \)

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

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