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Properties

Label 575.2.m
Level $575$
Weight $2$
Character orbit 575.m
Rep. character $\chi_{575}(22,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.m (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

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

Trace form

\( 464 q - 16 q^{2} - 12 q^{3} - 20 q^{4} - 12 q^{6} - 24 q^{8} - 20 q^{9} + O(q^{10}) \) \( 464 q - 16 q^{2} - 12 q^{3} - 20 q^{4} - 12 q^{6} - 24 q^{8} - 20 q^{9} - 4 q^{12} - 24 q^{13} + 92 q^{16} - 28 q^{18} + 10 q^{23} + 52 q^{25} - 32 q^{26} + 36 q^{27} - 60 q^{29} - 12 q^{31} - 44 q^{32} - 32 q^{35} - 140 q^{36} + 60 q^{39} - 12 q^{41} - 6 q^{46} + 28 q^{47} - 244 q^{48} + 100 q^{50} - 280 q^{52} - 280 q^{54} - 48 q^{55} - 56 q^{58} + 80 q^{59} + 140 q^{62} - 20 q^{64} - 80 q^{69} + 216 q^{70} - 52 q^{71} - 32 q^{72} - 44 q^{73} - 128 q^{75} - 88 q^{77} + 164 q^{78} + 112 q^{81} + 112 q^{82} - 16 q^{85} - 204 q^{87} - 78 q^{92} + 248 q^{93} - 20 q^{94} + 76 q^{95} + 124 q^{96} + 220 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
575.2.m.a 575.m 575.m $464$ $4.591$ None \(-16\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$