Properties

Label 175.1.c
Level $175$
Weight $1$
Character orbit 175.c
Rep. character $\chi_{175}(174,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 175.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(175, [\chi])\).

Total New Old
Modular forms 8 4 4
Cusp forms 2 2 0
Eisenstein series 6 2 4

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} - 2q^{11} + 2q^{14} - 2q^{16} + 2q^{29} + 2q^{46} - 2q^{49} + 2q^{56} - 2q^{64} - 2q^{71} - 2q^{74} + 2q^{79} + 2q^{81} + 2q^{86} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.1.c.a \(2\) \(0.087\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots\)