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Properties

Label 175.2.f
Level $175$
Weight $2$
Character orbit 175.f
Rep. character $\chi_{175}(118,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $4$
Sturm bound $40$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(11\)
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

\( 20 q + 4 q^{2} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 20 q + 4 q^{2} - 4 q^{7} + 8 q^{8} - 16 q^{11} - 48 q^{16} - 8 q^{18} + 8 q^{21} - 4 q^{22} - 8 q^{23} + 104 q^{36} + 24 q^{37} - 20 q^{42} + 12 q^{43} - 52 q^{46} - 64 q^{51} - 4 q^{53} + 68 q^{56} - 20 q^{57} - 12 q^{58} + 8 q^{63} + 4 q^{67} + 24 q^{71} + 16 q^{72} + 4 q^{77} + 20 q^{78} - 44 q^{81} - 132 q^{86} - 8 q^{88} + 48 q^{91} - 20 q^{93} + 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.f.a 175.f 35.f $4$ $1.397$ \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{3}-2\beta _{2}q^{4}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
175.2.f.b 175.f 35.f $4$ $1.397$ \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}-\beta _{1}q^{7}+3\beta _{3}q^{8}+\cdots\)
175.2.f.c 175.f 35.f $4$ $1.397$ \(\Q(i, \sqrt{10})\) None \(4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{6}+\cdots\)
175.2.f.d 175.f 35.f $8$ $1.397$ 8.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)

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

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