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Properties

Label 1428.2.ct
Level $1428$
Weight $2$
Character orbit 1428.ct
Rep. character $\chi_{1428}(185,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $384$
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.ct (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 357 \)
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 384 2016
Cusp forms 2208 384 1824
Eisenstein series 192 0 192

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 8 q^{15} - 48 q^{33} + 32 q^{37} - 8 q^{39} - 32 q^{43} - 36 q^{45} + 64 q^{49} + 24 q^{51} - 24 q^{63} - 96 q^{73} + 72 q^{75} - 16 q^{79} + 80 q^{85} - 72 q^{87} - 32 q^{91} + 60 q^{93} - 80 q^{99} + O(q^{100}) \)

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

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