Properties

Label 950.2.w
Level $950$
Weight $2$
Character orbit 950.w
Rep. character $\chi_{950}(37,\cdot)$
Character field $\Q(\zeta_{20})$
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.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 400q + 4q^{5} - 4q^{7} + O(q^{10}) \) \( 400q + 4q^{5} - 4q^{7} + 100q^{16} + 40q^{17} - 40q^{19} - 76q^{23} - 20q^{25} - 4q^{28} + 64q^{30} + 8q^{35} - 100q^{36} + 4q^{38} + 80q^{39} + 32q^{42} - 84q^{43} - 144q^{45} + 20q^{47} - 16q^{55} - 32q^{57} - 16q^{62} + 108q^{63} - 100q^{68} - 12q^{73} + 256q^{77} - 4q^{80} + 100q^{81} - 16q^{82} + 116q^{85} - 272q^{87} - 4q^{92} - 24q^{93} - 56q^{95} + O(q^{100}) \)

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.w.a \(400\) \(7.586\) None \(0\) \(0\) \(4\) \(-4\)

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

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