Properties

Label 667.2.j
Level $667$
Weight $2$
Character orbit 667.j
Rep. character $\chi_{667}(93,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $324$
Newform subspaces $2$
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.j (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
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 372 324 48
Cusp forms 348 324 24
Eisenstein series 24 0 24

Trace form

\( 324 q + 52 q^{4} - 4 q^{5} + 2 q^{6} + 8 q^{7} - 21 q^{8} + 42 q^{9} + O(q^{10}) \) \( 324 q + 52 q^{4} - 4 q^{5} + 2 q^{6} + 8 q^{7} - 21 q^{8} + 42 q^{9} - 8 q^{13} - 28 q^{15} - 48 q^{16} - 98 q^{18} + 8 q^{20} + 28 q^{21} + 24 q^{22} + 6 q^{23} + 16 q^{24} - 114 q^{25} + 28 q^{26} - 42 q^{27} - 96 q^{28} + 10 q^{29} + 44 q^{30} + 14 q^{31} + 28 q^{33} + 12 q^{34} - 12 q^{35} - 14 q^{36} - 42 q^{37} - 66 q^{38} - 14 q^{39} - 84 q^{40} - 90 q^{42} - 112 q^{44} - 70 q^{45} - 28 q^{47} - 21 q^{48} - 58 q^{49} + 98 q^{50} - 64 q^{51} + 34 q^{52} + 14 q^{53} + 93 q^{54} + 112 q^{55} + 98 q^{56} + 48 q^{57} + 115 q^{58} - 120 q^{59} + 84 q^{60} - 56 q^{61} - 32 q^{62} + 96 q^{63} + 193 q^{64} + 14 q^{65} - 168 q^{66} - 32 q^{67} + 14 q^{68} + 62 q^{71} - 112 q^{72} - 42 q^{73} - 24 q^{74} - 140 q^{76} - 70 q^{77} + 62 q^{78} + 2 q^{80} - 50 q^{81} + 74 q^{82} - 4 q^{83} - 168 q^{84} + 28 q^{86} + 36 q^{87} + 104 q^{88} + 70 q^{89} - 252 q^{90} - 8 q^{91} - 12 q^{92} + 36 q^{93} - 88 q^{94} - 56 q^{95} + 3 q^{96} - 70 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
667.2.j.a 667.j 29.e $144$ $5.326$ None \(0\) \(0\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{14}]$
667.2.j.b 667.j 29.e $180$ $5.326$ None \(0\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{14}]$

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

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