Properties

Label 950.3.d
Level $950$
Weight $3$
Character orbit 950.d
Rep. character $\chi_{950}(949,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $3$
Sturm bound $450$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 950.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(450\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(950, [\chi])\).

Total New Old
Modular forms 312 60 252
Cusp forms 288 60 228
Eisenstein series 24 0 24

Trace form

\( 60q + 120q^{4} + 180q^{9} + O(q^{10}) \) \( 60q + 120q^{4} + 180q^{9} - 36q^{11} + 240q^{16} - 20q^{19} - 64q^{26} + 360q^{36} + 56q^{39} - 72q^{44} - 360q^{49} + 288q^{54} + 324q^{61} + 480q^{64} + 288q^{66} - 40q^{76} + 1180q^{81} - 628q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
950.3.d.a \(4\) \(25.886\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-2\zeta_{8}^{2}q^{3}+2q^{4}-4q^{6}+\cdots\)
950.3.d.b \(24\) \(25.886\) None \(0\) \(0\) \(0\) \(0\)
950.3.d.c \(32\) \(25.886\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)