Properties

Label 950.2.bg
Level $950$
Weight $2$
Character orbit 950.bg
Rep. character $\chi_{950}(9,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $1200$
Newform subspaces $1$
Sturm bound $300$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bg (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Newform subspaces: \( 1 \)
Sturm bound: \(300\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

Total New Old
Modular forms 3696 1200 2496
Cusp forms 3504 1200 2304
Eisenstein series 192 0 192

Trace form

\( 1200q + O(q^{10}) \) \( 1200q + 18q^{11} + 90q^{15} + 12q^{20} - 60q^{22} - 60q^{23} - 96q^{25} - 36q^{29} - 60q^{33} + 30q^{35} - 120q^{45} - 60q^{46} - 60q^{47} + 660q^{49} - 24q^{50} + 120q^{51} + 36q^{54} + 36q^{55} + 48q^{56} - 36q^{59} - 30q^{60} - 144q^{61} - 150q^{64} + 120q^{65} + 96q^{66} + 48q^{69} - 60q^{70} - 120q^{71} - 48q^{79} - 96q^{81} - 30q^{83} + 78q^{84} - 192q^{85} + 60q^{87} - 72q^{89} - 36q^{90} + 60q^{92} - 96q^{94} - 24q^{95} - 180q^{97} - 240q^{98} - 192q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
950.2.bg.a \(1200\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)