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Properties

Label 1428.2.cw
Level $1428$
Weight $2$
Character orbit 1428.cw
Rep. character $\chi_{1428}(131,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $4480$
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.cw (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1428 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 4736 4736 0
Cusp forms 4480 4480 0
Eisenstein series 256 256 0

Trace form

\( 4480 q - 16 q^{4} - 16 q^{9} + O(q^{10}) \) \( 4480 q - 16 q^{4} - 16 q^{9} - 48 q^{10} - 24 q^{12} - 16 q^{18} - 32 q^{21} - 64 q^{22} - 24 q^{24} - 32 q^{25} + 16 q^{28} - 8 q^{30} - 32 q^{36} - 32 q^{37} - 48 q^{40} - 16 q^{42} - 48 q^{45} - 16 q^{46} - 64 q^{49} - 96 q^{52} - 144 q^{54} - 64 q^{57} - 16 q^{58} - 8 q^{60} - 96 q^{61} - 64 q^{64} - 24 q^{66} - 8 q^{72} - 96 q^{73} - 32 q^{78} - 16 q^{81} - 48 q^{82} - 128 q^{85} - 16 q^{88} - 16 q^{93} - 48 q^{94} - 24 q^{96} + O(q^{100}) \)

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.