↑

Properties

Label 2695.2.k
Level $2695$
Weight $2$
Character orbit 2695.k
Rep. character $\chi_{2695}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $472$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 704 512 192
Cusp forms 640 472 168
Eisenstein series 64 40 24

Trace form

\( 472 q + 2 q^{3} + 8 q^{5} + O(q^{10}) \) \( 472 q + 2 q^{3} + 8 q^{5} - 4 q^{11} - 24 q^{12} - 36 q^{15} - 396 q^{16} - 28 q^{22} - 10 q^{23} - 2 q^{25} - 24 q^{26} - 10 q^{27} + 24 q^{31} - 6 q^{33} - 380 q^{36} + 14 q^{37} + 64 q^{38} + 10 q^{45} + 28 q^{47} - 28 q^{48} + 32 q^{53} + 18 q^{55} + 96 q^{58} - 136 q^{60} - 104 q^{66} + 46 q^{67} - 44 q^{71} + 12 q^{75} + 112 q^{78} - 72 q^{80} - 276 q^{81} + 64 q^{82} + 128 q^{86} - 12 q^{88} + 64 q^{92} - 142 q^{93} + 106 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)