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Properties

Label 1428.2.co
Level $1428$
Weight $2$
Character orbit 1428.co
Rep. character $\chi_{1428}(25,\cdot)$
Character field $\Q(\zeta_{24})$
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.co (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2400 192 2208
Cusp forms 2208 192 2016
Eisenstein series 192 0 192

Trace form

\( 192 q - 8 q^{5} + O(q^{10}) \) \( 192 q - 8 q^{5} + 8 q^{11} + 16 q^{17} + 8 q^{25} + 32 q^{33} + 32 q^{35} - 32 q^{37} - 64 q^{41} + 32 q^{43} + 24 q^{49} - 64 q^{53} - 16 q^{59} - 24 q^{61} + 32 q^{65} - 16 q^{67} + 128 q^{69} - 32 q^{71} + 8 q^{73} - 48 q^{79} + 80 q^{83} - 64 q^{85} + 24 q^{87} + 64 q^{91} - 16 q^{93} + 24 q^{95} - 96 q^{97} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 2}\)