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Properties

Label 175.2.b
Level $175$
Weight $2$
Character orbit 175.b
Rep. character $\chi_{175}(99,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $40$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 26 10 16
Cusp forms 14 10 4
Eisenstein series 12 0 12

Trace form

\( 10 q - 4 q^{4} - 8 q^{6} - 14 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{4} - 8 q^{6} - 14 q^{9} + 4 q^{11} - 4 q^{14} + 8 q^{16} + 8 q^{19} + 28 q^{24} - 28 q^{29} - 20 q^{31} + 36 q^{34} - 20 q^{36} + 28 q^{39} + 8 q^{41} - 6 q^{44} - 34 q^{46} - 10 q^{49} - 4 q^{51} - 24 q^{54} + 18 q^{56} - 4 q^{59} + 16 q^{61} - 6 q^{64} + 8 q^{66} + 12 q^{69} + 40 q^{71} + 6 q^{74} - 52 q^{76} + 20 q^{79} + 18 q^{81} + 4 q^{84} + 42 q^{86} - 48 q^{89} - 4 q^{91} - 52 q^{94} + 20 q^{96} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.b.a 175.b 5.b $2$ $1.397$ \(\Q(\sqrt{-1}) \) None 35.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}-iq^{7}+2q^{9}-3q^{11}+\cdots\)
175.2.b.b 175.b 5.b $4$ $1.397$ \(\Q(i, \sqrt{17})\) None 35.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
175.2.b.c 175.b 5.b $4$ $1.397$ \(\Q(i, \sqrt{5})\) None 175.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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