Properties

Label 429.2.bv
Level $429$
Weight $2$
Character orbit 429.bv
Rep. character $\chi_{429}(20,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $832$
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{60})\)
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 960 960 0
Cusp forms 832 832 0
Eisenstein series 128 128 0

Trace form

\( 832q - 6q^{3} - 36q^{4} - 4q^{6} - 24q^{7} - 6q^{9} + O(q^{10}) \) \( 832q - 6q^{3} - 36q^{4} - 4q^{6} - 24q^{7} - 6q^{9} - 96q^{10} - 40q^{13} + 12q^{15} - 68q^{16} - 20q^{18} - 32q^{19} - 84q^{21} - 24q^{22} - 72q^{24} - 114q^{30} - 8q^{31} + 14q^{33} - 24q^{34} + 78q^{36} - 24q^{37} - 72q^{39} - 112q^{40} + 2q^{42} - 96q^{43} + 4q^{45} - 16q^{46} + 14q^{48} - 36q^{49} + 8q^{52} + 32q^{54} - 24q^{55} - 12q^{57} + 112q^{58} - 120q^{60} + 12q^{61} + 28q^{63} - 300q^{66} - 32q^{67} - 18q^{69} - 140q^{70} + 204q^{72} - 24q^{73} + 66q^{75} + 176q^{76} - 28q^{78} - 224q^{79} - 58q^{81} - 264q^{82} + 20q^{84} - 168q^{85} + 72q^{87} - 120q^{88} - 146q^{93} - 4q^{94} - 10q^{96} - 88q^{97} + 40q^{99} + O(q^{100}) \)

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.bv.a \(832\) \(3.426\) None \(0\) \(-6\) \(0\) \(-24\)