Properties

Label 950.2.x
Level $950$
Weight $2$
Character orbit 950.x
Rep. character $\chi_{950}(159,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $400$
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.x (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
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 1232 400 832
Cusp forms 1168 400 768
Eisenstein series 64 0 64

Trace form

\( 400q - 50q^{4} + 2q^{5} - 50q^{9} + O(q^{10}) \) \( 400q - 50q^{4} + 2q^{5} - 50q^{9} - 12q^{11} + 8q^{14} - 18q^{15} + 50q^{16} - 10q^{17} - 12q^{19} + 4q^{20} - 32q^{21} + 20q^{22} + 30q^{23} - 14q^{25} + 60q^{27} + 24q^{29} - 52q^{30} + 20q^{33} + 8q^{34} - 8q^{35} + 50q^{36} - 24q^{39} - 16q^{41} + 4q^{44} - 144q^{45} - 32q^{46} + 120q^{47} - 440q^{49} - 40q^{50} + 52q^{51} + 40q^{53} - 12q^{54} - 88q^{55} + 16q^{56} + 48q^{59} - 2q^{60} - 28q^{61} + 10q^{63} + 100q^{64} + 152q^{65} + 16q^{66} - 80q^{67} - 16q^{69} + 8q^{70} - 14q^{71} + 80q^{73} - 104q^{75} - 8q^{76} - 80q^{77} + 60q^{78} - 8q^{79} + 2q^{80} + 106q^{81} + 80q^{83} + 56q^{84} + 78q^{85} - 20q^{86} + 80q^{87} + 12q^{89} + 78q^{90} - 8q^{91} - 20q^{92} + 4q^{95} - 30q^{97} - 40q^{98} - 12q^{99} + O(q^{100}) \)

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.x.a \(400\) \(7.586\) None \(0\) \(0\) \(2\) \(0\)

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

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