↑

Properties

Label 3040.2.cf
Level $3040$
Weight $2$
Character orbit 3040.cf
Rep. character $\chi_{3040}(1027,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1728$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3040.cf (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

Total New Old
Modular forms 1936 1728 208
Cusp forms 1904 1728 176
Eisenstein series 32 0 32

Trace form

\( 1728 q + O(q^{10}) \) \( 1728 q + 32 q^{12} + 32 q^{22} + 32 q^{24} - 80 q^{30} - 80 q^{42} + 64 q^{43} - 32 q^{44} + 40 q^{48} - 1728 q^{49} + 104 q^{52} + 112 q^{54} + 64 q^{55} - 96 q^{56} + 64 q^{58} - 72 q^{62} - 96 q^{64} - 32 q^{66} - 72 q^{70} - 64 q^{71} - 120 q^{72} - 152 q^{78} + 88 q^{80} - 80 q^{82} - 216 q^{88} - 352 q^{90} - 224 q^{92} - 32 q^{96} + 88 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)