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Properties

Label 2790.2.dn
Level $2790$
Weight $2$
Character orbit 2790.dn
Rep. character $\chi_{2790}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1024$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.dn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 279 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

Total New Old
Modular forms 4672 1024 3648
Cusp forms 4544 1024 3520
Eisenstein series 128 0 128

Trace form

\( 1024 q - 128 q^{4} + 4 q^{7} + O(q^{10}) \) \( 1024 q - 128 q^{4} + 4 q^{7} + 128 q^{16} + 16 q^{18} + 8 q^{19} + 12 q^{21} - 36 q^{23} + 512 q^{25} + 24 q^{26} + 84 q^{27} + 36 q^{28} + 4 q^{31} - 28 q^{33} - 8 q^{39} - 24 q^{41} + 28 q^{43} + 8 q^{45} + 132 q^{49} - 80 q^{51} + 192 q^{53} + 192 q^{57} - 84 q^{61} + 144 q^{62} - 24 q^{63} + 256 q^{64} + 16 q^{66} - 28 q^{67} - 64 q^{69} - 48 q^{71} + 32 q^{72} - 84 q^{73} + 24 q^{74} - 24 q^{76} + 180 q^{77} - 56 q^{78} - 28 q^{79} + 272 q^{81} + 144 q^{83} + 16 q^{84} + 144 q^{86} + 148 q^{87} + 72 q^{89} + 48 q^{90} + 20 q^{91} + 36 q^{92} - 12 q^{93} - 24 q^{95} + 24 q^{97} - 192 q^{98} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)