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Properties

Label 2352.2.cn
Level $2352$
Weight $2$
Character orbit 2352.cn
Rep. character $\chi_{2352}(125,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $5328$
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.cn (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2352 \)
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 5424 0
Cusp forms 5328 5328 0
Eisenstein series 96 96 0

Trace form

\( 5328 q - 14 q^{3} - 20 q^{4} - 14 q^{6} + O(q^{10}) \) \( 5328 q - 14 q^{3} - 20 q^{4} - 14 q^{6} - 28 q^{10} - 14 q^{12} - 28 q^{13} - 20 q^{15} - 20 q^{16} + 4 q^{18} - 6 q^{21} - 44 q^{22} - 14 q^{24} - 14 q^{27} - 112 q^{28} - 32 q^{30} - 28 q^{33} + 84 q^{34} - 26 q^{36} - 20 q^{37} - 140 q^{40} + 10 q^{42} - 20 q^{43} - 14 q^{45} - 4 q^{46} - 48 q^{49} + 42 q^{51} - 28 q^{52} - 14 q^{54} - 52 q^{58} - 134 q^{60} - 28 q^{61} - 52 q^{63} + 28 q^{64} + 126 q^{66} - 48 q^{67} - 14 q^{69} + 52 q^{70} + 22 q^{72} - 14 q^{75} - 364 q^{76} - 78 q^{78} - 96 q^{79} - 20 q^{81} - 168 q^{82} - 120 q^{84} + 20 q^{85} - 20 q^{88} - 14 q^{90} + 148 q^{91} + 20 q^{93} - 196 q^{94} + 476 q^{96} + 12 q^{99} + O(q^{100}) \)

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.