Properties

Label 175.4.a
Level $175$
Weight $4$
Character orbit 175.a
Rep. character $\chi_{175}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $10$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(175))\).

Total New Old
Modular forms 66 29 37
Cusp forms 54 29 25
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(17\)
Minus space\(-\)\(12\)

Trace form

\( 29 q - 5 q^{2} + 6 q^{3} + 137 q^{4} - 22 q^{6} - 7 q^{7} - 33 q^{8} + 233 q^{9} + 88 q^{11} + 190 q^{12} - 44 q^{13} + 63 q^{14} + 369 q^{16} + 142 q^{17} + 335 q^{18} - 110 q^{19} - 14 q^{21} - 20 q^{22}+ \cdots + 7276 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(175))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7
175.4.a.a 175.a 1.a $1$ $10.325$ \(\Q\) None 35.4.a.a \(-1\) \(8\) \(0\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+8q^{3}-7q^{4}-8q^{6}-7q^{7}+\cdots\)
175.4.a.b 175.a 1.a $1$ $10.325$ \(\Q\) None 7.4.a.a \(1\) \(2\) \(0\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-7q^{4}+2q^{6}+7q^{7}+\cdots\)
175.4.a.c 175.a 1.a $2$ $10.325$ \(\Q(\sqrt{2}) \) None 35.4.a.b \(-8\) \(-2\) \(0\) \(14\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-4+\beta )q^{2}+(-1-4\beta )q^{3}+(10+\cdots)q^{4}+\cdots\)
175.4.a.d 175.a 1.a $2$ $10.325$ \(\Q(\sqrt{41}) \) None 175.4.a.d \(-1\) \(5\) \(0\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{3}+(2+\beta )q^{4}+(-10+\cdots)q^{6}+\cdots\)
175.4.a.e 175.a 1.a $2$ $10.325$ \(\Q(\sqrt{41}) \) None 175.4.a.d \(1\) \(-5\) \(0\) \(14\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-2-\beta )q^{3}+(2+\beta )q^{4}+(-10+\cdots)q^{6}+\cdots\)
175.4.a.f 175.a 1.a $3$ $10.325$ 3.3.14360.1 None 35.4.a.c \(3\) \(-2\) \(0\) \(-21\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
175.4.a.g 175.a 1.a $4$ $10.325$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 175.4.a.g \(-4\) \(3\) \(0\) \(-28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
175.4.a.h 175.a 1.a $4$ $10.325$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 175.4.a.g \(4\) \(-3\) \(0\) \(28\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
175.4.a.i 175.a 1.a $5$ $10.325$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 35.4.b.a \(-4\) \(-10\) \(0\) \(-35\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
175.4.a.j 175.a 1.a $5$ $10.325$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 35.4.b.a \(4\) \(10\) \(0\) \(35\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(175)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)