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Properties

Label 2352.4.cr
Level $2352$
Weight $4$
Character orbit 2352.cr
Rep. character $\chi_{2352}(139,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $8064$
Sturm bound $1792$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.cr (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

Total New Old
Modular forms 16176 8064 8112
Cusp forms 16080 8064 8016
Eisenstein series 96 0 96

Trace form

\( 8064 q + 168 q^{8} + O(q^{10}) \) \( 8064 q + 168 q^{8} - 208 q^{14} - 504 q^{22} + 164 q^{28} - 1008 q^{34} + 456 q^{35} + 1008 q^{40} + 660 q^{42} - 6160 q^{44} + 1400 q^{46} + 2856 q^{50} - 1540 q^{56} - 728 q^{58} - 6888 q^{64} - 3696 q^{67} + 3704 q^{70} + 2240 q^{71} - 4312 q^{74} - 4284 q^{76} + 3528 q^{78} + 108864 q^{81} + 12180 q^{82} - 1800 q^{84} - 4116 q^{86} + 1540 q^{88} + 9104 q^{91} - 3668 q^{92} + 7560 q^{94} - 22540 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)