↑

Properties

Label 3450.2.x
Level $3450$
Weight $2$
Character orbit 3450.x
Rep. character $\chi_{3450}(367,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3450.x (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3450, [\chi])\).

Total New Old
Modular forms 5824 960 4864
Cusp forms 5696 960 4736
Eisenstein series 128 0 128

Trace form

\( 960 q + O(q^{10}) \) \( 960 q - 16 q^{13} + 240 q^{16} + 72 q^{23} + 32 q^{25} - 160 q^{29} - 64 q^{35} - 240 q^{36} + 48 q^{47} - 16 q^{50} - 16 q^{52} - 48 q^{55} + 160 q^{59} + 64 q^{62} + 160 q^{70} - 96 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 240 q^{81} + 112 q^{82} + 48 q^{85} - 112 q^{87} - 8 q^{92} + 32 q^{93} + 112 q^{95} + 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)