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Properties

Label 670.2.q
Level $670$
Weight $2$
Character orbit 670.q
Rep. character $\chi_{670}(21,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $480$
Newform subspaces $4$
Sturm bound $204$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.q (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 4 \)
Sturm bound: \(204\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 2120 480 1640
Cusp forms 1960 480 1480
Eisenstein series 160 0 160

Trace form

\( 480 q - 2 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 64 q^{9} + O(q^{10}) \) \( 480 q - 2 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 64 q^{9} + 24 q^{12} + 4 q^{13} - 12 q^{14} + 24 q^{16} + 28 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{20} + 20 q^{21} + 40 q^{22} - 12 q^{23} + 14 q^{24} - 48 q^{25} - 4 q^{27} + 4 q^{28} + 38 q^{29} + 42 q^{30} + 36 q^{31} - 2 q^{32} + 4 q^{33} + 10 q^{34} + 4 q^{35} + 32 q^{36} + 52 q^{37} + 114 q^{38} + 84 q^{39} - 6 q^{41} - 8 q^{42} + 4 q^{43} + 8 q^{45} + 18 q^{46} + 8 q^{47} + 2 q^{48} + 42 q^{49} - 2 q^{50} + 30 q^{51} + 36 q^{52} - 8 q^{53} - 140 q^{54} - 12 q^{55} + 6 q^{56} - 234 q^{57} - 152 q^{58} - 106 q^{59} + 138 q^{61} - 104 q^{62} - 224 q^{63} - 48 q^{64} - 8 q^{65} + 60 q^{66} - 112 q^{67} - 100 q^{68} - 150 q^{69} + 62 q^{70} - 24 q^{71} + 8 q^{72} - 318 q^{73} - 80 q^{74} + 18 q^{75} - 12 q^{76} - 160 q^{77} - 164 q^{78} - 116 q^{79} - 2 q^{80} + 32 q^{81} - 140 q^{82} - 66 q^{83} - 2 q^{84} + 144 q^{87} - 20 q^{88} + 116 q^{89} + 24 q^{91} + 24 q^{92} + 88 q^{93} + 56 q^{94} + 12 q^{95} + 4 q^{96} + 122 q^{97} + 54 q^{98} + 268 q^{99} + O(q^{100}) \)

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.q.a 670.q 67.g $100$ $5.350$ None \(5\) \(-2\) \(-10\) \(4\) $\mathrm{SU}(2)[C_{33}]$
670.2.q.b 670.q 67.g $120$ $5.350$ None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{33}]$
670.2.q.c 670.q 67.g $120$ $5.350$ None \(6\) \(-4\) \(12\) \(1\) $\mathrm{SU}(2)[C_{33}]$
670.2.q.d 670.q 67.g $140$ $5.350$ None \(-7\) \(2\) \(14\) \(-1\) $\mathrm{SU}(2)[C_{33}]$

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

\( S_{2}^{\mathrm{old}}(670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)