Properties

Label 175.2.k
Level $175$
Weight $2$
Character orbit 175.k
Rep. character $\chi_{175}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

Total New Old
Modular forms 52 28 24
Cusp forms 28 20 8
Eisenstein series 24 8 16

Trace form

\( 20q + 10q^{4} - 16q^{6} + 8q^{9} + O(q^{10}) \) \( 20q + 10q^{4} - 16q^{6} + 8q^{9} - 4q^{11} - 26q^{14} - 2q^{16} - 8q^{19} + 6q^{21} - 16q^{24} - 6q^{26} + 40q^{29} + 14q^{31} - 4q^{36} + 32q^{39} - 44q^{41} - 12q^{44} + 16q^{46} - 44q^{49} - 14q^{51} - 42q^{54} - 6q^{56} - 26q^{59} + 2q^{61} + 120q^{64} - 44q^{66} - 24q^{69} - 4q^{71} - 30q^{74} + 124q^{76} + 34q^{79} + 30q^{81} + 2q^{84} + 48q^{86} - 24q^{89} - 62q^{91} - 26q^{94} - 14q^{96} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.2.k.a \(8\) \(1.397\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+(1-\zeta_{24}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
175.2.k.b \(12\) \(1.397\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{10}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)