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Properties

Label 3456.2.ci
Level $3456$
Weight $2$
Character orbit 3456.ci
Rep. character $\chi_{3456}(35,\cdot)$
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.ci (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

\( 6080 q + 48 q^{2} - 16 q^{4} + 48 q^{5} - 16 q^{7} + O(q^{10}) \) \( 6080 q + 48 q^{2} - 16 q^{4} + 48 q^{5} - 16 q^{7} - 64 q^{10} + 48 q^{11} - 16 q^{13} + 48 q^{14} - 16 q^{16} - 64 q^{19} + 48 q^{20} - 16 q^{22} + 48 q^{23} - 16 q^{25} - 64 q^{28} + 48 q^{29} - 16 q^{31} + 48 q^{32} - 16 q^{34} - 64 q^{37} + 48 q^{38} - 16 q^{40} + 48 q^{41} - 16 q^{43} - 64 q^{46} + 48 q^{47} - 16 q^{49} + 48 q^{50} - 16 q^{52} - 64 q^{55} + 48 q^{56} - 160 q^{58} + 48 q^{59} - 16 q^{61} - 64 q^{64} - 16 q^{67} + 48 q^{68} - 16 q^{70} - 64 q^{73} + 48 q^{74} + 80 q^{76} + 48 q^{77} - 16 q^{79} - 64 q^{82} + 48 q^{83} - 16 q^{85} + 48 q^{86} - 16 q^{88} - 64 q^{91} + 48 q^{92} - 16 q^{94} + 48 q^{95} - 16 q^{97} + O(q^{100}) \)

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

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