↑

Properties

Label 2805.2.dp
Level $2805$
Weight $2$
Character orbit 2805.dp
Rep. character $\chi_{2805}(38,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3392$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2805.dp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2805 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2805, [\chi])\).

Total New Old
Modular forms 3520 3520 0
Cusp forms 3392 3392 0
Eisenstein series 128 128 0

Trace form

\( 3392 q - 12 q^{3} - 12 q^{6} - 24 q^{7} + 24 q^{9} + O(q^{10}) \) \( 3392 q - 12 q^{3} - 12 q^{6} - 24 q^{7} + 24 q^{9} - 16 q^{10} - 32 q^{13} - 24 q^{15} + 752 q^{16} - 28 q^{18} - 64 q^{21} - 48 q^{24} - 12 q^{25} - 12 q^{27} - 12 q^{30} - 8 q^{31} - 16 q^{33} - 32 q^{39} + 12 q^{40} + 24 q^{42} - 32 q^{43} - 36 q^{45} - 48 q^{46} + 92 q^{48} - 752 q^{49} + 76 q^{51} - 8 q^{52} - 64 q^{54} - 48 q^{55} + 12 q^{57} - 84 q^{60} - 48 q^{61} + 44 q^{63} - 64 q^{67} - 168 q^{70} - 92 q^{72} - 88 q^{73} + 6 q^{75} - 40 q^{79} - 48 q^{81} + 12 q^{85} - 24 q^{87} - 64 q^{88} - 52 q^{90} + 32 q^{91} + 24 q^{93} + 80 q^{94} + 4 q^{96} - 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2805, [\chi])\) into newform subspaces

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