Properties

Label 950.2.bi
Level $950$
Weight $2$
Character orbit 950.bi
Rep. character $\chi_{950}(3,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $2400$
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.bi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{180})\)
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 7392 2400 4992
Cusp forms 7008 2400 4608
Eisenstein series 384 0 384

Trace form

\( 2400q + 12q^{7} + O(q^{10}) \) \( 2400q + 12q^{7} + 36q^{15} - 36q^{17} + 96q^{22} + 120q^{23} + 24q^{25} - 120q^{29} - 24q^{33} - 36q^{35} - 168q^{43} + 36q^{45} - 96q^{47} + 144q^{50} - 36q^{53} + 72q^{55} + 156q^{57} - 120q^{59} + 24q^{60} + 24q^{62} - 36q^{63} - 720q^{65} + 96q^{67} + 12q^{68} + 48q^{70} + 36q^{73} - 96q^{78} - 48q^{82} - 84q^{83} - 540q^{84} - 288q^{85} - 192q^{87} - 168q^{90} - 72q^{92} - 156q^{93} - 24q^{95} - 120q^{97} - 24q^{98} + O(q^{100}) \)

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.bi.a \(2400\) \(7.586\) None \(0\) \(0\) \(0\) \(12\)

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

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