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Properties

Label 2352.3.dq
Level $2352$
Weight $3$
Character orbit 2352.dq
Rep. character $\chi_{2352}(163,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $10752$
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.dq (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
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 10752 10848
Cusp forms 21408 10752 10656
Eisenstein series 192 0 192

Trace form

\( 10752 q - 24 q^{8} + O(q^{10}) \) \( 10752 q - 24 q^{8} + 36 q^{10} + 32 q^{14} + 160 q^{20} + 24 q^{22} + 300 q^{28} - 400 q^{34} + 96 q^{35} + 280 q^{38} + 580 q^{40} - 60 q^{42} - 1408 q^{44} - 180 q^{46} - 288 q^{48} - 312 q^{50} + 24 q^{52} + 56 q^{56} - 92 q^{58} + 128 q^{59} + 1008 q^{62} - 312 q^{64} - 72 q^{66} - 288 q^{67} + 260 q^{68} + 132 q^{70} - 2560 q^{71} + 220 q^{74} + 300 q^{76} + 360 q^{78} + 1840 q^{80} - 8064 q^{81} + 2080 q^{82} + 72 q^{84} - 244 q^{86} + 5148 q^{88} + 192 q^{91} + 1216 q^{92} + 1044 q^{94} + 300 q^{96} - 944 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)