Properties

Label 429.2.bq
Level $429$
Weight $2$
Character orbit 429.bq
Rep. character $\chi_{429}(29,\cdot)$
Character field $\Q(\zeta_{30})$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 416q - 3q^{3} + 42q^{4} - 5q^{6} - 10q^{7} + 3q^{9} + O(q^{10}) \) \( 416q - 3q^{3} + 42q^{4} - 5q^{6} - 10q^{7} + 3q^{9} - 52q^{12} - 20q^{13} - 3q^{15} + 30q^{16} - 20q^{18} - 10q^{19} + 4q^{22} + 5q^{24} + 60q^{25} - 24q^{27} - 10q^{28} - 65q^{30} - 8q^{31} + 49q^{33} - 24q^{34} + 3q^{36} - 6q^{37} - 35q^{39} - 120q^{40} - 13q^{42} - 32q^{45} - 30q^{46} - 33q^{48} - 26q^{49} - 100q^{51} - 60q^{52} - 42q^{55} - 20q^{57} - 34q^{58} + 32q^{60} - 30q^{61} - 45q^{63} + 40q^{64} + 42q^{66} + 32q^{67} - 33q^{69} - 268q^{70} + 55q^{72} - 40q^{73} + 9q^{75} - 32q^{78} - 37q^{81} + 28q^{82} - 180q^{84} - 10q^{85} - 142q^{88} - 30q^{90} + 8q^{91} - 26q^{93} - 90q^{94} + 330q^{96} - 14q^{97} - 4q^{99} + O(q^{100}) \)

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.bq.a \(416\) \(3.426\) None \(0\) \(-3\) \(0\) \(-10\)