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Properties

Label 2695.2.da
Level $2695$
Weight $2$
Character orbit 2695.da
Rep. character $\chi_{2695}(12,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $6720$
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.da (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 8160 6720 1440
Cusp forms 7968 6720 1248
Eisenstein series 192 0 192

Trace form

\( 6720 q - 56 q^{6} + 24 q^{8} + O(q^{10}) \) \( 6720 q - 56 q^{6} + 24 q^{8} - 24 q^{15} - 552 q^{16} + 36 q^{17} + 56 q^{21} + 76 q^{28} - 24 q^{30} - 24 q^{31} - 192 q^{32} + 12 q^{35} + 1000 q^{36} - 12 q^{38} + 48 q^{40} - 112 q^{41} - 88 q^{42} - 32 q^{43} - 36 q^{45} - 312 q^{46} + 72 q^{47} + 432 q^{50} + 108 q^{52} - 24 q^{56} - 60 q^{57} - 32 q^{58} - 40 q^{60} - 248 q^{61} + 104 q^{63} + 8 q^{67} + 144 q^{68} - 412 q^{70} - 96 q^{71} - 480 q^{72} - 96 q^{73} + 120 q^{75} + 312 q^{78} - 108 q^{80} - 136 q^{81} + 208 q^{82} - 420 q^{83} - 48 q^{85} + 56 q^{86} + 36 q^{87} + 168 q^{90} + 112 q^{91} + 72 q^{92} - 848 q^{93} + 24 q^{95} - 672 q^{96} + 36 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)