Properties

Label 670.2.k
Level $670$
Weight $2$
Character orbit 670.k
Rep. character $\chi_{670}(81,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $200$
Newform subspaces $4$
Sturm bound $204$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.k (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{11})\)
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 1060 200 860
Cusp forms 980 200 780
Eisenstein series 80 0 80

Trace form

\( 200 q + 2 q^{2} + 8 q^{3} - 20 q^{4} + 2 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} - 4 q^{9} + O(q^{10}) \) \( 200 q + 2 q^{2} + 8 q^{3} - 20 q^{4} + 2 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} - 4 q^{9} + 12 q^{11} - 14 q^{12} + 28 q^{13} + 12 q^{14} - 20 q^{16} + 2 q^{17} + 10 q^{18} + 32 q^{19} + 2 q^{20} - 6 q^{21} + 20 q^{22} + 12 q^{23} - 14 q^{24} - 20 q^{25} + 32 q^{27} + 16 q^{28} - 20 q^{29} - 36 q^{30} - 4 q^{31} + 2 q^{32} + 8 q^{33} + 20 q^{34} + 8 q^{35} - 4 q^{36} - 8 q^{37} - 108 q^{38} - 76 q^{39} + 24 q^{41} + 32 q^{42} + 64 q^{43} + 12 q^{44} + 10 q^{45} + 36 q^{46} + 52 q^{47} + 8 q^{48} + 72 q^{49} + 2 q^{50} + 72 q^{51} - 60 q^{52} + 32 q^{53} + 14 q^{54} + 24 q^{55} + 12 q^{56} - 36 q^{57} - 52 q^{58} - 98 q^{59} - 10 q^{61} - 4 q^{62} - 196 q^{63} - 20 q^{64} + 8 q^{65} - 12 q^{66} - 22 q^{67} - 20 q^{68} - 24 q^{69} - 50 q^{70} + 60 q^{71} + 10 q^{72} - 132 q^{73} - 4 q^{74} - 14 q^{75} + 32 q^{76} - 56 q^{77} - 40 q^{78} - 64 q^{79} + 2 q^{80} - 100 q^{81} - 22 q^{82} - 42 q^{83} - 28 q^{84} + 12 q^{85} + 24 q^{86} - 36 q^{87} + 20 q^{88} + 124 q^{89} + 136 q^{91} + 12 q^{92} - 32 q^{93} + 16 q^{94} + 24 q^{95} + 8 q^{96} + 36 q^{97} - 54 q^{98} - 88 q^{99} + O(q^{100}) \)

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.k.a 670.k 67.e $40$ $5.350$ None \(-4\) \(6\) \(-4\) \(13\) $\mathrm{SU}(2)[C_{11}]$
670.2.k.b 670.k 67.e $50$ $5.350$ None \(-5\) \(2\) \(5\) \(1\) $\mathrm{SU}(2)[C_{11}]$
670.2.k.c 670.k 67.e $50$ $5.350$ None \(5\) \(-2\) \(-5\) \(-1\) $\mathrm{SU}(2)[C_{11}]$
670.2.k.d 670.k 67.e $60$ $5.350$ None \(6\) \(2\) \(6\) \(3\) $\mathrm{SU}(2)[C_{11}]$

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

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