Properties

Label 950.2.bd
Level $950$
Weight $2$
Character orbit 950.bd
Rep. character $\chi_{950}(27,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $800$
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.bd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
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 2464 800 1664
Cusp forms 2336 800 1536
Eisenstein series 128 0 128

Trace form

\( 800q - 4q^{5} - 8q^{7} + O(q^{10}) \) \( 800q - 4q^{5} - 8q^{7} - 36q^{15} - 100q^{16} - 4q^{17} + 40q^{19} - 96q^{22} - 44q^{23} - 4q^{25} + 4q^{28} + 120q^{29} - 64q^{30} + 132q^{33} + 28q^{35} + 100q^{36} - 4q^{38} - 80q^{39} - 32q^{42} - 36q^{43} + 216q^{45} + 76q^{47} + 36q^{53} + 88q^{55} - 124q^{57} + 120q^{59} + 48q^{60} - 8q^{62} - 72q^{63} - 24q^{67} + 88q^{68} + 24q^{70} - 24q^{73} - 256q^{77} + 24q^{78} + 4q^{80} - 100q^{81} - 8q^{82} - 24q^{83} + 28q^{85} - 112q^{87} - 12q^{90} + 4q^{92} - 108q^{93} - 28q^{95} + 12q^{97} - 120q^{98} + O(q^{100}) \)

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.bd.a \(800\) \(7.586\) None \(0\) \(0\) \(-4\) \(-8\)

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

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