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Properties

Label 175.3.m
Level $175$
Weight $3$
Character orbit 175.m
Rep. character $\chi_{175}(34,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $152$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 175.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(175, [\chi])\).

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

Trace form

\( 152 q - 10 q^{2} + 66 q^{4} - 40 q^{8} - 108 q^{9} + O(q^{10}) \) \( 152 q - 10 q^{2} + 66 q^{4} - 40 q^{8} - 108 q^{9} + 24 q^{11} - 21 q^{14} + 60 q^{15} - 150 q^{16} - 50 q^{22} - 180 q^{23} + 20 q^{25} - 45 q^{28} + 24 q^{29} + 170 q^{30} - 155 q^{35} + 136 q^{36} - 10 q^{37} + 250 q^{39} - 305 q^{42} + 202 q^{44} - 342 q^{46} - 178 q^{49} + 260 q^{50} - 220 q^{51} - 60 q^{53} + 78 q^{56} + 50 q^{58} + 100 q^{60} + 190 q^{63} + 424 q^{64} - 220 q^{65} + 710 q^{67} + 270 q^{70} - 236 q^{71} + 690 q^{72} + 28 q^{74} + 360 q^{77} + 80 q^{78} + 374 q^{79} - 688 q^{81} - 370 q^{84} + 490 q^{85} - 522 q^{86} - 2620 q^{88} - 170 q^{91} + 440 q^{92} - 880 q^{95} + 65 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.3.m.a 175.m 175.m $152$ $4.768$ None \(-10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$