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Properties

Label 667.2.g
Level $667$
Weight $2$
Character orbit 667.g
Rep. character $\chi_{667}(24,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $336$
Newform subspaces $3$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.g (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(667, [\chi])\).

Total New Old
Modular forms 372 336 36
Cusp forms 348 336 12
Eisenstein series 24 0 24

Trace form

\( 336q - 2q^{2} - 58q^{4} - 8q^{5} - 10q^{6} - 8q^{7} + 9q^{8} - 68q^{9} + O(q^{10}) \) \( 336q - 2q^{2} - 58q^{4} - 8q^{5} - 10q^{6} - 8q^{7} + 9q^{8} - 68q^{9} - 20q^{10} - 8q^{11} - 6q^{12} - 20q^{13} - 8q^{14} - 62q^{16} - 36q^{17} + 54q^{18} + 22q^{20} + 8q^{21} - 6q^{23} - 64q^{24} - 24q^{25} + 24q^{26} + 18q^{27} + 48q^{28} - 4q^{29} + 44q^{30} - 6q^{31} - 26q^{32} - 44q^{33} + 38q^{34} - 44q^{35} - 108q^{36} - 10q^{37} + 50q^{38} + 18q^{39} + 38q^{40} - 40q^{41} + 90q^{42} - 8q^{43} + 8q^{44} + 56q^{45} - 12q^{47} - 69q^{48} - 108q^{49} + 40q^{50} - 40q^{51} - 86q^{52} + 28q^{53} - 27q^{54} + 44q^{55} + 46q^{56} - 48q^{57} + 77q^{58} + 144q^{59} + 12q^{60} - 32q^{61} - 68q^{62} - 133q^{64} + 24q^{65} + 28q^{66} + 18q^{68} - 80q^{70} - 66q^{71} - 24q^{72} + 96q^{73} - 60q^{74} - 16q^{75} + 24q^{76} + 2q^{77} - 46q^{78} - 72q^{79} + 218q^{80} + 4q^{81} - 62q^{82} + 76q^{83} - 76q^{84} - 132q^{85} - 116q^{86} + 4q^{87} + 8q^{88} + 2q^{89} + 16q^{90} + 8q^{91} - 12q^{92} + 28q^{93} - 12q^{94} + 40q^{95} + 107q^{96} + 32q^{97} + 54q^{98} + 108q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(667, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
667.2.g.a \(6\) \(5.326\) \(\Q(\zeta_{14})\) None \(-2\) \(1\) \(2\) \(-13\) \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
667.2.g.b \(144\) \(5.326\) None \(1\) \(-1\) \(-2\) \(19\)
667.2.g.c \(186\) \(5.326\) None \(-1\) \(0\) \(-8\) \(-14\)

Decomposition of \(S_{2}^{\mathrm{old}}(667, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(667, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)