Properties

Label 429.2.be
Level $429$
Weight $2$
Character orbit 429.be
Rep. character $\chi_{429}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $184$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).

Total New Old
Modular forms 240 184 56
Cusp forms 208 184 24
Eisenstein series 32 0 32

Trace form

\( 184 q - 12 q^{6} + 12 q^{7} + O(q^{10}) \) \( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
429.2.be.a 429.be 39.k $184$ $3.426$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(429, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)