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Properties

Label 700.2.bo
Level $700$
Weight $2$
Character orbit 700.bo
Rep. character $\chi_{700}(9,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $160$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{30})\)
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 1008 160 848
Cusp forms 912 160 752
Eisenstein series 96 0 96

Trace form

\( 160 q + q^{5} - 20 q^{9} + O(q^{10}) \) \( 160 q + q^{5} - 20 q^{9} + 3 q^{11} - 34 q^{15} + 10 q^{17} + 4 q^{19} + 6 q^{21} + 9 q^{25} + 60 q^{27} - 12 q^{29} - 6 q^{31} + 25 q^{33} - 2 q^{39} + 14 q^{41} + 40 q^{45} - 6 q^{49} + 12 q^{51} - 50 q^{53} - 54 q^{55} + 24 q^{59} - 14 q^{61} - 16 q^{65} + 10 q^{69} - 34 q^{71} - 40 q^{73} - 83 q^{75} + 40 q^{77} - 20 q^{79} + 16 q^{81} + 50 q^{83} - 120 q^{85} + 9 q^{89} - 46 q^{91} - q^{95} - 20 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bo.a 700.bo 175.t $160$ $5.590$ None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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