↑

Properties

Label 3150.2.dy
Level $3150$
Weight $2$
Character orbit 3150.dy
Rep. character $\chi_{3150}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.dy (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q + 240 q^{4} + O(q^{10}) \) \( 1920 q + 240 q^{4} + 38 q^{15} + 240 q^{16} - 12 q^{21} - 2 q^{30} - 150 q^{33} - 30 q^{35} + 32 q^{39} - 18 q^{45} + 36 q^{50} + 12 q^{51} + 10 q^{60} - 180 q^{62} - 100 q^{63} - 480 q^{64} + 54 q^{65} + 48 q^{66} + 126 q^{69} + 24 q^{70} + 30 q^{75} + 12 q^{79} + 52 q^{81} - 36 q^{84} + 90 q^{89} + 216 q^{90} + 60 q^{92} - 66 q^{95} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)