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Properties

Label 700.2.bq
Level $700$
Weight $2$
Character orbit 700.bq
Rep. character $\chi_{700}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $928$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
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 992 992 0
Cusp forms 928 928 0
Eisenstein series 64 64 0

Trace form

\( 928 q - 3 q^{2} - 3 q^{4} - 24 q^{5} - 30 q^{8} + 102 q^{9} + O(q^{10}) \) \( 928 q - 3 q^{2} - 3 q^{4} - 24 q^{5} - 30 q^{8} + 102 q^{9} - 21 q^{10} - 9 q^{12} - 18 q^{14} - 3 q^{16} - 18 q^{17} - 10 q^{18} + 6 q^{21} - 4 q^{22} - 42 q^{24} - 12 q^{25} - 36 q^{26} + 8 q^{28} - 24 q^{29} - 39 q^{30} - 28 q^{32} - 42 q^{33} + 20 q^{36} - 6 q^{37} - 36 q^{38} - 27 q^{40} - 32 q^{42} + 13 q^{44} - 42 q^{45} - 15 q^{46} - 24 q^{49} + 38 q^{50} - 114 q^{52} - 6 q^{53} - 33 q^{54} + 54 q^{56} - 56 q^{57} - 51 q^{58} - 57 q^{60} - 18 q^{61} - 42 q^{64} - 26 q^{65} + 9 q^{66} - 90 q^{68} + 23 q^{70} + 96 q^{72} - 18 q^{73} - 38 q^{74} - 30 q^{77} - 158 q^{78} - 276 q^{80} + 66 q^{81} - 96 q^{82} + 87 q^{84} - 52 q^{85} - 17 q^{86} - 22 q^{88} - 18 q^{89} + 58 q^{92} - 104 q^{93} - 9 q^{94} - 99 q^{96} + 106 q^{98} + O(q^{100}) \)

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.bq.a 700.bq 700.aq $928$ $5.590$ None \(-3\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{30}]$