Properties

Label 475.3.d
Level $475$
Weight $3$
Character orbit 475.d
Rep. character $\chi_{475}(474,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $4$
Sturm bound $150$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(150\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

Total New Old
Modular forms 106 62 44
Cusp forms 94 58 36
Eisenstein series 12 4 8

Trace form

\( 58q + 108q^{4} - 12q^{6} + 166q^{9} + O(q^{10}) \) \( 58q + 108q^{4} - 12q^{6} + 166q^{9} + 22q^{11} + 132q^{16} - 32q^{19} + 148q^{24} + 224q^{26} + 64q^{36} - 140q^{39} + 232q^{44} - 468q^{49} - 304q^{54} - 102q^{61} - 64q^{64} - 32q^{66} - 400q^{74} - 142q^{76} - 182q^{81} + 760q^{96} + 770q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.3.d.a \(2\) \(12.943\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q-4q^{4}-iq^{7}-9q^{9}+3q^{11}+2^{4}q^{16}+\cdots\)
475.3.d.b \(4\) \(12.943\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{3}q^{3}+9q^{4}+13q^{6}+\beta _{1}q^{7}+\cdots\)
475.3.d.c \(24\) \(12.943\) None \(0\) \(0\) \(0\) \(0\)
475.3.d.d \(28\) \(12.943\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

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