↑

Properties

Label 2550.2.cn
Level $2550$
Weight $2$
Character orbit 2550.cn
Rep. character $\chi_{2550}(37,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $2880$
Sturm bound $1080$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2550.cn (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2550, [\chi])\).

Total New Old
Modular forms 17536 2880 14656
Cusp forms 17024 2880 14144
Eisenstein series 512 0 512

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q - 16 q^{10} - 32 q^{25} - 32 q^{28} + 32 q^{33} - 32 q^{37} - 80 q^{41} + 160 q^{46} - 64 q^{50} - 32 q^{52} + 64 q^{53} - 32 q^{55} - 64 q^{57} + 32 q^{67} + 32 q^{70} + 16 q^{72} + 80 q^{73} + 80 q^{74} + 64 q^{75} + 96 q^{77} + 64 q^{78} + 320 q^{79} + 32 q^{80} + 224 q^{83} - 64 q^{85} + 96 q^{87} + 32 q^{88} + 32 q^{92} - 64 q^{93} - 32 q^{97} + 144 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2550, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)