Properties

Label 175.1.d
Level $175$
Weight $1$
Character orbit 175.d
Rep. character $\chi_{175}(76,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $20$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 8 5 3
Cusp forms 2 2 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 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.d.a \(1\) \(0.087\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)
175.1.d.b \(1\) \(0.087\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)