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Properties

Label 350.2.r
Level $350$
Weight $2$
Character orbit 350.r
Rep. character $\chi_{350}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $160$
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.r (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 \(M_{2}(350, [\chi])\).

Total New Old
Modular forms 512 160 352
Cusp forms 448 160 288
Eisenstein series 64 0 64

Trace form

\( 160 q + 8 q^{7} + O(q^{10}) \) \( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98} + O(q^{100}) \)

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.r.a 350.r 175.s $160$ $2.795$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{20}]$

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

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