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Properties

Label 2352.2.cr
Level $2352$
Weight $2$
Character orbit 2352.cr
Rep. character $\chi_{2352}(139,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2688$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.cr (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 5424 2688 2736
Cusp forms 5328 2688 2640
Eisenstein series 96 0 96

Trace form

\( 2688 q - 24 q^{8} + O(q^{10}) \) \( 2688 q - 24 q^{8} + 16 q^{14} + 24 q^{22} + 52 q^{28} + 112 q^{34} - 24 q^{35} + 112 q^{40} - 20 q^{42} - 80 q^{44} + 40 q^{46} + 24 q^{50} + 28 q^{56} + 88 q^{58} + 24 q^{64} - 48 q^{67} + 40 q^{70} - 320 q^{71} + 88 q^{74} + 84 q^{76} + 24 q^{78} + 448 q^{81} + 140 q^{82} + 24 q^{84} - 60 q^{86} - 220 q^{88} - 176 q^{91} - 100 q^{92} - 168 q^{94} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)