Properties

Label 429.2.bm
Level $429$
Weight $2$
Character orbit 429.bm
Rep. character $\chi_{429}(17,\cdot)$
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.bm (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

\( 416q - 3q^{3} - 54q^{4} - 15q^{6} - 30q^{7} - 9q^{9} + O(q^{10}) \) \( 416q - 3q^{3} - 54q^{4} - 15q^{6} - 30q^{7} - 9q^{9} - 36q^{12} - 20q^{13} - 9q^{15} + 14q^{16} - 30q^{19} - 28q^{22} + 15q^{24} - 84q^{25} - 24q^{27} - 30q^{28} - 5q^{30} - 27q^{33} - 73q^{36} - 18q^{37} - 65q^{39} - 120q^{40} - 25q^{42} + 36q^{45} + 30q^{46} - 41q^{48} + 14q^{49} + 60q^{51} + 20q^{52} + 18q^{55} - 126q^{58} - 30q^{61} + 105q^{63} - 56q^{64} + 170q^{66} - 33q^{69} - 195q^{72} + 77q^{75} + 4q^{78} - 13q^{81} + 36q^{82} - 60q^{84} - 30q^{85} + 38q^{88} - 190q^{90} - 56q^{91} + 24q^{93} - 90q^{94} + 54q^{97} + O(q^{100}) \)

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.bm.a \(416\) \(3.426\) None \(0\) \(-3\) \(0\) \(-30\)