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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
429.2.be.a \(184\) \(3.426\) None \(0\) \(0\) \(0\) \(12\)

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

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