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Properties

Label 3456.2.cg
Level $3456$
Weight $2$
Character orbit 3456.cg
Rep. character $\chi_{3456}(49,\cdot)$
Character field $\Q(\zeta_{72})$
Dimension $3408$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.cg (of order \(72\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 864 \)
Character field: \(\Q(\zeta_{72})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 14016 3504 10512
Cusp forms 13632 3408 10224
Eisenstein series 384 96 288

Trace form

\( 3408 q + 24 q^{3} - 24 q^{5} + 24 q^{7} - 24 q^{9} + O(q^{10}) \) \( 3408 q + 24 q^{3} - 24 q^{5} + 24 q^{7} - 24 q^{9} + 24 q^{11} - 24 q^{13} + 12 q^{19} - 24 q^{21} + 24 q^{23} - 24 q^{25} + 24 q^{27} - 24 q^{29} + 48 q^{31} - 48 q^{33} + 12 q^{35} - 12 q^{37} + 24 q^{39} - 24 q^{41} + 24 q^{43} - 24 q^{45} + 60 q^{51} - 48 q^{53} + 48 q^{55} - 24 q^{57} + 24 q^{59} - 24 q^{61} + 48 q^{63} - 48 q^{65} + 24 q^{67} - 24 q^{69} + 12 q^{71} - 12 q^{73} + 24 q^{75} - 24 q^{77} + 144 q^{83} - 84 q^{85} + 24 q^{87} - 12 q^{89} + 12 q^{91} - 24 q^{93} + 48 q^{95} - 48 q^{97} + 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)