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Properties

Label 2695.2.cq
Level $2695$
Weight $2$
Character orbit 2695.cq
Rep. character $\chi_{2695}(18,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3712$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.cq (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2695, [\chi])\).

Total New Old
Modular forms 5632 3968 1664
Cusp forms 5120 3712 1408
Eisenstein series 512 256 256

Trace form

\( 3712 q + 10 q^{2} + 6 q^{3} + 2 q^{5} + 80 q^{6} - 80 q^{8} + O(q^{10}) \) \( 3712 q + 10 q^{2} + 6 q^{3} + 2 q^{5} + 80 q^{6} - 80 q^{8} + 12 q^{11} + 40 q^{13} - 24 q^{15} - 412 q^{16} + 30 q^{17} + 10 q^{18} - 8 q^{20} - 112 q^{22} + 32 q^{23} + 50 q^{25} + 36 q^{26} + 10 q^{30} + 12 q^{31} - 32 q^{33} + 480 q^{36} + 50 q^{37} + 22 q^{38} - 70 q^{40} + 200 q^{41} - 56 q^{45} + 260 q^{46} - 34 q^{47} + 208 q^{48} - 80 q^{50} + 220 q^{51} + 10 q^{52} - 14 q^{53} + 56 q^{55} + 80 q^{57} + 94 q^{58} - 14 q^{60} - 60 q^{61} + 40 q^{62} + 8 q^{66} - 16 q^{67} - 90 q^{68} - 256 q^{71} + 70 q^{72} + 130 q^{73} - 58 q^{75} - 664 q^{78} + 2 q^{80} - 252 q^{81} - 2 q^{82} + 40 q^{83} - 240 q^{85} + 100 q^{86} + 54 q^{88} - 460 q^{90} + 64 q^{92} + 38 q^{93} + 160 q^{96} + 64 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2695, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2695, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)