Properties

Label 950.2.f
Level $950$
Weight $2$
Character orbit 950.f
Rep. character $\chi_{950}(493,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $4$
Sturm bound $300$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(300\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 324 60 264
Cusp forms 276 60 216
Eisenstein series 48 0 48

Trace form

\( 60q - 4q^{7} + O(q^{10}) \) \( 60q - 4q^{7} - 16q^{11} - 60q^{16} + 20q^{17} + 4q^{23} + 16q^{26} - 4q^{28} + 60q^{36} + 4q^{38} + 32q^{42} - 4q^{43} - 60q^{47} + 48q^{57} - 16q^{61} - 16q^{62} + 28q^{63} + 88q^{66} + 20q^{68} - 12q^{73} - 64q^{77} - 60q^{81} - 16q^{82} - 20q^{83} + 8q^{87} - 4q^{92} - 104q^{93} + O(q^{100}) \)

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.f.a \(4\) \(7.586\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots\)
950.2.f.b \(8\) \(7.586\) 8.0.3317760000.4 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+q^{6}+\beta _{3}q^{7}+\cdots\)
950.2.f.c \(16\) \(7.586\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{9}q^{2}+\beta _{13}q^{3}+\beta _{1}q^{4}+\beta _{2}q^{6}+\cdots\)
950.2.f.d \(32\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)