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Properties

Label 3456.2.cl
Level $3456$
Weight $2$
Character orbit 3456.cl
Rep. character $\chi_{3456}(37,\cdot)$
Character field $\Q(\zeta_{96})$
Dimension $6080$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.cl (of order \(96\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1152 \)
Character field: \(\Q(\zeta_{96})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3456, [\chi])\).

Total New Old
Modular forms 18624 6208 12416
Cusp forms 18240 6080 12160
Eisenstein series 384 128 256

Trace form

\( 6080 q + 16 q^{2} - 16 q^{4} + 16 q^{5} - 16 q^{7} + 64 q^{8} + O(q^{10}) \) \( 6080 q + 16 q^{2} - 16 q^{4} + 16 q^{5} - 16 q^{7} + 64 q^{8} - 64 q^{10} + 16 q^{11} - 16 q^{13} + 16 q^{14} - 16 q^{16} + 64 q^{17} - 64 q^{19} + 16 q^{20} - 16 q^{22} + 16 q^{23} - 16 q^{25} + 64 q^{26} - 64 q^{28} + 16 q^{29} - 16 q^{31} + 16 q^{32} - 16 q^{34} + 64 q^{35} - 64 q^{37} + 16 q^{38} - 16 q^{40} + 16 q^{41} - 16 q^{43} + 64 q^{44} - 64 q^{46} + 16 q^{47} - 16 q^{49} + 16 q^{50} - 16 q^{52} + 64 q^{53} - 64 q^{55} + 16 q^{56} + 128 q^{58} + 16 q^{59} - 16 q^{61} + 64 q^{62} - 64 q^{64} - 16 q^{67} + 16 q^{68} - 16 q^{70} + 64 q^{71} - 64 q^{73} + 16 q^{74} - 112 q^{76} + 16 q^{77} - 16 q^{79} + 64 q^{80} - 64 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{88} + 64 q^{89} - 64 q^{91} + 16 q^{92} - 16 q^{94} + 16 q^{95} - 16 q^{97} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)