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Properties

Label 175.2.e
Level $175$
Weight $2$
Character orbit 175.e
Rep. character $\chi_{175}(51,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $5$
Sturm bound $40$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(40\)
Trace bound: \(2\)
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 32 20
Cusp forms 28 20 8
Eisenstein series 24 12 12

Trace form

\( 20 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 16 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 16 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{9} - 6 q^{12} + 8 q^{13} + 22 q^{14} + 6 q^{16} + 4 q^{17} - 8 q^{18} - 4 q^{19} - 18 q^{21} + 8 q^{22} - 2 q^{23} + 12 q^{24} - 22 q^{26} - 4 q^{27} + 22 q^{28} - 8 q^{29} - 2 q^{31} - 6 q^{32} + 12 q^{33} - 16 q^{34} + 36 q^{36} + 8 q^{38} - 24 q^{39} - 4 q^{41} + 2 q^{42} - 20 q^{43} + 24 q^{46} + 4 q^{47} - 12 q^{48} + 8 q^{49} - 14 q^{51} - 20 q^{52} - 8 q^{53} + 38 q^{54} - 18 q^{56} + 16 q^{57} - 2 q^{58} - 2 q^{59} - 18 q^{61} + 24 q^{62} - 64 q^{64} - 48 q^{66} + 22 q^{67} + 20 q^{68} + 48 q^{69} + 4 q^{71} - 8 q^{72} + 4 q^{73} + 46 q^{74} + 68 q^{76} - 28 q^{77} - 8 q^{78} - 6 q^{79} + 26 q^{81} - 18 q^{82} - 4 q^{83} - 22 q^{84} + 40 q^{86} - 2 q^{87} + 4 q^{88} - 38 q^{91} - 12 q^{92} - 12 q^{93} + 30 q^{94} - 14 q^{96} - 24 q^{97} + 14 q^{98} - 12 q^{99} + O(q^{100}) \)

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.e.a 175.e 7.c $2$ $1.397$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.b 175.e 7.c $2$ $1.397$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.c 175.e 7.c $4$ $1.397$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
175.2.e.d 175.e 7.c $6$ $1.397$ 6.0.1783323.2 None \(-1\) \(3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
175.2.e.e 175.e 7.c $6$ $1.397$ 6.0.1783323.2 None \(1\) \(-3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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