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Properties

Label 2352.3.cq
Level $2352$
Weight $3$
Character orbit 2352.cq
Rep. character $\chi_{2352}(83,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $10704$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.cq (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2352 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 10800 10800 0
Cusp forms 10704 10704 0
Eisenstein series 96 96 0

Trace form

\( 10704 q - 14 q^{3} - 20 q^{4} - 14 q^{6} - 48 q^{7} + O(q^{10}) \) \( 10704 q - 14 q^{3} - 20 q^{4} - 14 q^{6} - 48 q^{7} - 28 q^{10} - 14 q^{12} - 28 q^{13} - 20 q^{16} - 108 q^{18} - 30 q^{21} + 4 q^{22} - 14 q^{24} - 14 q^{27} - 320 q^{28} - 8 q^{30} - 28 q^{33} - 588 q^{34} - 74 q^{36} - 20 q^{37} - 20 q^{39} + 756 q^{40} - 294 q^{42} - 20 q^{43} - 14 q^{45} - 52 q^{46} - 48 q^{49} + 186 q^{51} - 28 q^{52} - 14 q^{54} - 56 q^{55} - 372 q^{58} - 774 q^{60} - 28 q^{61} + 28 q^{64} + 1526 q^{66} - 48 q^{67} - 14 q^{69} - 268 q^{70} + 246 q^{72} - 14 q^{75} - 1708 q^{76} + 50 q^{78} - 20 q^{81} + 1792 q^{82} - 1328 q^{84} + 180 q^{85} - 28 q^{87} - 20 q^{88} - 14 q^{90} - 796 q^{91} - 100 q^{93} - 1204 q^{94} - 1540 q^{96} + 300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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