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Properties

Label 670.2.v
Level $670$
Weight $2$
Character orbit 670.v
Rep. character $\chi_{670}(19,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $680$
Newform subspaces $1$
Sturm bound $204$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.v (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 335 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(204\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(670, [\chi])\).

Total New Old
Modular forms 2120 680 1440
Cusp forms 1960 680 1280
Eisenstein series 160 0 160

Trace form

\( 680 q - 34 q^{4} - 4 q^{5} - 2 q^{6} + 48 q^{9} + O(q^{10}) \) \( 680 q - 34 q^{4} - 4 q^{5} - 2 q^{6} + 48 q^{9} - 4 q^{11} - 4 q^{14} + 36 q^{15} + 34 q^{16} - 64 q^{19} - 2 q^{20} - 28 q^{21} + 18 q^{24} + 4 q^{25} - 6 q^{29} + 12 q^{34} - 2 q^{35} + 24 q^{36} + 122 q^{41} + 4 q^{44} + 62 q^{45} - 18 q^{46} - 32 q^{49} - 8 q^{50} + 28 q^{51} - 22 q^{54} + 164 q^{55} - 2 q^{56} + 112 q^{59} + 84 q^{60} - 442 q^{61} + 68 q^{64} + 178 q^{65} - 488 q^{66} - 46 q^{69} + 66 q^{70} - 300 q^{71} + 12 q^{74} + 48 q^{75} - 128 q^{76} + 116 q^{79} + 24 q^{80} - 412 q^{81} + 94 q^{84} - 16 q^{85} - 34 q^{86} - 148 q^{89} + 26 q^{90} - 88 q^{91} - 80 q^{94} + 100 q^{95} - 2 q^{96} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(670, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
670.2.v.a 670.v 335.u $680$ $5.350$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{66}]$

Decomposition of \(S_{2}^{\mathrm{old}}(670, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)