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Properties

Label 350.2.x
Level $350$
Weight $2$
Character orbit 350.x
Rep. character $\chi_{350}(3,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $320$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.x (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

Total New Old
Modular forms 1024 320 704
Cusp forms 896 320 576
Eisenstein series 128 0 128

Trace form

\( 320 q + 12 q^{5} - 8 q^{7} + O(q^{10}) \) \( 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.2.x.a 350.x 175.x $320$ $2.795$ None \(0\) \(0\) \(12\) \(-8\) $\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)