↑

Properties

Label 175.5.g
Level $175$
Weight $5$
Character orbit 175.g
Rep. character $\chi_{175}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $4$
Sturm bound $100$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(100\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(175, [\chi])\).

Total New Old
Modular forms 172 72 100
Cusp forms 148 72 76
Eisenstein series 24 0 24

Trace form

\( 72 q - 20 q^{3} - 144 q^{6} + O(q^{10}) \) \( 72 q - 20 q^{3} - 144 q^{6} - 312 q^{11} + 80 q^{12} + 560 q^{13} - 4720 q^{16} - 1320 q^{17} - 340 q^{18} - 392 q^{21} + 2020 q^{22} - 1920 q^{23} - 10176 q^{26} + 340 q^{27} + 4224 q^{31} + 1200 q^{32} + 6140 q^{33} + 18112 q^{36} - 3980 q^{37} - 9120 q^{38} - 4128 q^{41} - 4900 q^{42} + 12220 q^{43} + 31100 q^{46} + 11820 q^{47} + 4040 q^{48} - 11720 q^{51} - 3600 q^{52} - 24240 q^{53} - 5292 q^{56} - 6460 q^{57} - 6100 q^{58} + 14960 q^{61} + 16680 q^{62} - 7840 q^{63} + 55616 q^{66} + 5940 q^{67} + 47040 q^{68} + 30024 q^{71} - 46720 q^{72} + 2500 q^{73} - 95632 q^{76} - 5880 q^{77} + 17940 q^{78} - 159680 q^{81} + 32120 q^{82} - 15120 q^{83} + 44436 q^{86} + 25460 q^{87} - 52920 q^{88} + 22344 q^{91} - 19800 q^{92} - 1460 q^{93} + 90624 q^{96} + 33840 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.5.g.a 175.g 5.c $4$ $18.090$ \(\Q(i, \sqrt{14})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-6\beta _{3}q^{3}-9\beta _{2}q^{4}+42q^{6}+\cdots\)
175.5.g.b 175.g 5.c $12$ $18.090$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}+(-3\beta _{5}+2\beta _{7})q^{3}+\cdots\)
175.5.g.c 175.g 5.c $24$ $18.090$ None \(0\) \(-20\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
175.5.g.d 175.g 5.c $32$ $18.090$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)