Properties

Label 670.2.e
Level 670
Weight 2
Character orbit e
Rep. character \(\chi_{670}(171,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 48
Newforms 10
Sturm bound 204
Trace bound 9

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Defining parameters

Level: \( N \) = \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 670.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 10 \)
Sturm bound: \(204\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 212 48 164
Cusp forms 196 48 148
Eisenstein series 16 0 16

Trace form

\( 48q + 2q^{2} + 4q^{3} - 24q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} + 64q^{9} + O(q^{10}) \) \( 48q + 2q^{2} + 4q^{3} - 24q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} + 64q^{9} - 2q^{12} - 4q^{13} + 12q^{14} - 24q^{16} - 6q^{17} + 4q^{18} - 6q^{19} + 2q^{20} + 2q^{21} - 40q^{22} + 12q^{23} + 8q^{24} + 48q^{25} + 4q^{27} - 4q^{28} + 6q^{29} + 2q^{30} + 8q^{31} + 2q^{32} - 4q^{33} - 10q^{34} - 4q^{35} - 32q^{36} - 8q^{37} + 18q^{38} + 48q^{39} + 6q^{41} + 8q^{42} - 4q^{43} - 8q^{45} - 18q^{46} - 8q^{47} - 2q^{48} - 42q^{49} + 2q^{50} - 30q^{51} + 8q^{52} - 80q^{53} + 8q^{54} + 12q^{55} - 6q^{56} + 58q^{57} - 24q^{58} - 4q^{59} - 28q^{61} + 16q^{62} - 40q^{63} + 48q^{64} + 8q^{65} - 16q^{66} - 64q^{67} + 12q^{68} - 26q^{69} + 4q^{70} + 24q^{71} - 8q^{72} - 34q^{73} - 8q^{74} + 4q^{75} + 12q^{76} - 16q^{77} - 12q^{78} - 16q^{79} + 2q^{80} + 144q^{81} + 8q^{82} + 2q^{84} - 12q^{87} + 20q^{88} - 116q^{89} - 24q^{91} - 24q^{92} + 88q^{93} - 12q^{94} - 12q^{95} - 4q^{96} - 34q^{97} + 34q^{98} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(670, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
670.2.e.a \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-2\) \(2\) \(q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
670.2.e.b \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
670.2.e.c \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(-2\) \(5\) \(q+(-1+\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
670.2.e.d \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-2\) \(-2\) \(q+(1-\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
670.2.e.e \(4\) \(5.350\) \(\Q(\sqrt{-3}, \sqrt{193})\) None \(-2\) \(4\) \(-4\) \(-4\) \(q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
670.2.e.f \(4\) \(5.350\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(-4\) \(-4\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-1+\beta _{1})q^{4}+\cdots\)
670.2.e.g \(6\) \(5.350\) 6.0.954288.1 None \(3\) \(-2\) \(6\) \(-2\) \(q+(1-\beta _{3})q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+q^{5}+\cdots\)
670.2.e.h \(6\) \(5.350\) 6.0.2696112.1 None \(3\) \(2\) \(6\) \(2\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+q^{5}+\cdots\)
670.2.e.i \(8\) \(5.350\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(8\) \(8\) \(0\) \(q+(-1+\beta _{2})q^{2}+(1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
670.2.e.j \(12\) \(5.350\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-4\) \(-12\) \(3\) \(q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{5})q^{4}-q^{5}+\cdots\)

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

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