↑

Properties

Label 2352.3.cu
Level $2352$
Weight $3$
Character orbit 2352.cu
Rep. character $\chi_{2352}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $5376$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.cu (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
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 5376 5424
Cusp forms 10704 5376 5328
Eisenstein series 96 0 96

Trace form

\( 5376 q - 24 q^{8} + O(q^{10}) \) \( 5376 q - 24 q^{8} - 16 q^{14} - 24 q^{22} + 420 q^{28} - 560 q^{34} - 96 q^{35} - 784 q^{40} - 60 q^{42} + 880 q^{44} - 360 q^{46} - 312 q^{50} + 28 q^{56} + 520 q^{58} + 408 q^{64} + 576 q^{67} - 72 q^{70} - 440 q^{74} + 420 q^{76} + 360 q^{78} + 8064 q^{81} - 1820 q^{82} - 72 q^{84} + 572 q^{86} - 1980 q^{88} + 192 q^{91} - 1076 q^{92} - 1176 q^{94} - 1536 q^{95} - 700 q^{98} + O(q^{100}) \)

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

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