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Properties

Label 2352.3.do
Level $2352$
Weight $3$
Character orbit 2352.do
Rep. character $\chi_{2352}(59,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $21408$
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.do (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2352 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 21600 21600 0
Cusp forms 21408 21408 0
Eisenstein series 192 192 0

Trace form

\( 21408 q - 22 q^{3} - 52 q^{4} - 28 q^{6} - 96 q^{7} + O(q^{10}) \) \( 21408 q - 22 q^{3} - 52 q^{4} - 28 q^{6} - 96 q^{7} - 44 q^{10} - 22 q^{12} - 56 q^{13} - 52 q^{16} - 78 q^{18} - 72 q^{19} - 6 q^{21} - 64 q^{22} - 22 q^{24} - 28 q^{27} + 248 q^{28} - 4 q^{30} - 44 q^{33} + 504 q^{34} + 44 q^{36} - 52 q^{37} - 52 q^{39} - 888 q^{40} + 42 q^{42} - 40 q^{43} - 22 q^{45} - 20 q^{46} - 96 q^{49} + 18 q^{51} - 440 q^{52} - 106 q^{54} - 112 q^{55} - 228 q^{58} + 1062 q^{60} - 44 q^{61} - 88 q^{64} - 902 q^{66} - 24 q^{67} - 28 q^{69} + 52 q^{70} + 102 q^{72} + 128 q^{75} + 1624 q^{76} - 80 q^{78} - 52 q^{81} - 1132 q^{82} - 3856 q^{84} - 240 q^{85} - 44 q^{87} - 52 q^{88} - 28 q^{90} + 136 q^{91} + 64 q^{93} + 1744 q^{94} + 2116 q^{96} - 372 q^{99} + O(q^{100}) \)

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.