Properties

Label 475.1.c
Level $475$
Weight $1$
Character orbit 475.c
Rep. character $\chi_{475}(151,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $50$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 475.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(50\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(475, [\chi])\).

Total New Old
Modular forms 9 6 3
Cusp forms 3 3 0
Eisenstein series 6 3 3

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{4} - 4 q^{6} - q^{9} + O(q^{10}) \) \( 3 q - q^{4} - 4 q^{6} - q^{9} - 2 q^{11} - q^{16} + q^{19} + 4 q^{26} + 3 q^{36} + 4 q^{39} - 2 q^{44} - 3 q^{49} - 2 q^{61} + 3 q^{64} + 4 q^{74} - 3 q^{76} - q^{81} + 4 q^{96} - 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.1.c.a 475.c 19.b $1$ $0.237$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) 95.1.d.a \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots\)
475.1.c.b 475.c 19.b $2$ $0.237$ \(\Q(\sqrt{-2}) \) $D_{4}$ \(\Q(\sqrt{-95}) \) None 95.1.d.b \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}-q^{9}+\beta q^{12}+\cdots\)