Properties

Label 700.2.bv
Level $700$
Weight $2$
Character orbit 700.bv
Rep. character $\chi_{700}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $320$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).

Total New Old
Modular forms 2016 320 1696
Cusp forms 1824 320 1504
Eisenstein series 192 0 192

Trace form

\( 320 q - 6 q^{5} - 2 q^{7} + O(q^{10}) \) \( 320 q - 6 q^{5} - 2 q^{7} + 20 q^{15} - 18 q^{17} - 4 q^{23} - 6 q^{25} + 40 q^{29} + 42 q^{33} + 50 q^{35} + 14 q^{37} - 40 q^{39} + 52 q^{43} - 174 q^{45} + 6 q^{47} - 70 q^{53} + 116 q^{57} - 120 q^{59} - 98 q^{63} - 34 q^{65} - 8 q^{67} - 78 q^{73} + 144 q^{75} - 90 q^{77} - 40 q^{81} - 30 q^{87} + 150 q^{89} + 22 q^{93} + 38 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
700.2.bv.a 700.bv 175.x $320$ $5.590$ None \(0\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)