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Properties

Label 3564.2.ce
Level $3564$
Weight $2$
Character orbit 3564.ce
Rep. character $\chi_{3564}(25,\cdot)$
Character field $\Q(\zeta_{135})$
Dimension $7776$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3564.ce (of order \(135\) and degree \(72\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 891 \)
Character field: \(\Q(\zeta_{135})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3564, [\chi])\).

Total New Old
Modular forms 47088 7776 39312
Cusp forms 46224 7776 38448
Eisenstein series 864 0 864

Trace form

\( 7776 q + O(q^{10}) \) \( 7776 q - 54 q^{23} - 54 q^{27} + 81 q^{29} - 27 q^{33} + 108 q^{45} + 126 q^{51} - 189 q^{59} + 180 q^{65} + 108 q^{67} + 90 q^{75} + 144 q^{77} - 108 q^{79} - 108 q^{85} + 288 q^{87} - 342 q^{89} + 18 q^{93} - 27 q^{97} + 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3564, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3564, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3564, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(891, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1782, [\chi])\)\(^{\oplus 2}\)