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Properties

Label 175.4.s
Level $175$
Weight $4$
Character orbit 175.s
Rep. character $\chi_{175}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 16 q^{2} - 20 q^{4} - 132 q^{8} - 20 q^{9} + O(q^{10}) \) \( 464 q - 16 q^{2} - 20 q^{4} - 132 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} + 320 q^{15} + 1652 q^{16} - 172 q^{18} - 6 q^{21} - 896 q^{22} - 152 q^{23} + 280 q^{25} + 1238 q^{28} - 100 q^{29} - 1240 q^{30} - 452 q^{32} - 960 q^{35} + 2932 q^{36} - 136 q^{37} - 2460 q^{39} + 1570 q^{42} - 1152 q^{43} - 20 q^{44} - 12 q^{46} - 8140 q^{50} - 32 q^{51} + 1520 q^{53} - 262 q^{56} + 4300 q^{57} + 4328 q^{58} - 4120 q^{60} + 1060 q^{63} + 9640 q^{64} - 1680 q^{65} - 3416 q^{67} - 3310 q^{70} - 12 q^{71} - 9496 q^{72} - 1426 q^{77} - 6340 q^{78} - 20 q^{79} + 6792 q^{81} + 13190 q^{84} + 1440 q^{85} - 12 q^{86} + 7524 q^{88} - 6 q^{91} + 6308 q^{92} + 11300 q^{93} - 9740 q^{95} - 17602 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.4.s.a 175.s 175.s $464$ $10.325$ None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$