Properties

Label 429.2.bi
Level $429$
Weight $2$
Character orbit 429.bi
Rep. character $\chi_{429}(5,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $416$
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.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{20})\)
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 480 480 0
Cusp forms 416 416 0
Eisenstein series 64 64 0

Trace form

\( 416q - 12q^{3} - 14q^{6} - 12q^{7} - 12q^{9} + O(q^{10}) \) \( 416q - 12q^{3} - 14q^{6} - 12q^{7} - 12q^{9} - 20q^{13} - 30q^{15} + 32q^{16} + 2q^{18} - 4q^{19} - 12q^{21} - 24q^{22} - 78q^{24} - 36q^{27} - 84q^{28} - 28q^{31} - 44q^{33} - 24q^{34} - 12q^{37} + 54q^{39} + 88q^{40} - 56q^{42} + 8q^{45} - 92q^{46} + 40q^{48} - 44q^{52} - 176q^{54} - 72q^{55} - 6q^{57} - 4q^{58} + 12q^{60} - 48q^{61} - 46q^{63} + 204q^{66} - 64q^{67} + 56q^{70} - 66q^{72} - 12q^{73} - 104q^{76} - 92q^{78} + 104q^{79} + 124q^{81} + 16q^{84} - 12q^{85} - 24q^{87} - 84q^{91} - 124q^{93} + 328q^{94} - 152q^{96} + 52q^{97} - 142q^{99} + O(q^{100}) \)

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.bi.a \(416\) \(3.426\) None \(0\) \(-12\) \(0\) \(-12\)