↑

Properties

Label 3150.2.eo
Level $3150$
Weight $2$
Character orbit 3150.eo
Rep. character $\chi_{3150}(317,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
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.eo (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11648 3840 7808
Cusp forms 11392 3840 7552
Eisenstein series 256 0 256

Trace form

\( 3840 q + O(q^{10}) \) \( 3840 q - 12 q^{15} - 480 q^{16} - 36 q^{17} - 16 q^{18} - 36 q^{27} + 12 q^{30} + 20 q^{33} + 40 q^{39} + 4 q^{42} + 140 q^{45} + 48 q^{50} - 32 q^{57} - 24 q^{58} - 8 q^{60} + 228 q^{63} - 24 q^{65} + 140 q^{69} - 8 q^{72} - 232 q^{75} + 48 q^{77} + 16 q^{78} + 120 q^{84} - 40 q^{87} + 300 q^{89} + 80 q^{90} + 24 q^{92} + 12 q^{93} + O(q^{100}) \)

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

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