Properties

Label 429.2.bn
Level $429$
Weight $2$
Character orbit 429.bn
Rep. character $\chi_{429}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $224$
Newform subspaces $2$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).

Total New Old
Modular forms 480 224 256
Cusp forms 416 224 192
Eisenstein series 64 0 64

Trace form

\( 224q - 28q^{4} + 28q^{9} + O(q^{10}) \) \( 224q - 28q^{4} + 28q^{9} - 40q^{10} + 36q^{11} + 16q^{12} - 14q^{13} + 24q^{14} - 12q^{15} + 24q^{16} + 8q^{17} - 24q^{19} - 24q^{20} - 26q^{22} + 20q^{23} + 44q^{25} - 48q^{26} + 36q^{28} - 12q^{29} + 20q^{30} + 6q^{33} + 4q^{35} - 28q^{36} + 68q^{38} - 8q^{39} - 40q^{40} + 36q^{41} - 12q^{42} - 96q^{43} + 36q^{46} - 40q^{48} - 80q^{49} + 60q^{50} - 56q^{51} - 2q^{52} - 68q^{53} - 16q^{55} - 176q^{56} + 120q^{58} + 54q^{59} - 12q^{61} + 8q^{62} - 32q^{64} + 52q^{65} - 56q^{66} - 20q^{68} - 14q^{69} + 48q^{71} + 52q^{74} + 32q^{75} - 264q^{76} - 132q^{77} - 40q^{78} + 72q^{79} - 48q^{80} + 28q^{81} + 34q^{82} - 60q^{85} + 112q^{87} + 80q^{88} - 216q^{89} - 40q^{90} - 78q^{91} + 68q^{92} - 24q^{93} - 28q^{94} + 132q^{95} - 162q^{97} + 96q^{98} + O(q^{100}) \)

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.bn.a \(112\) \(3.426\) None \(0\) \(-14\) \(0\) \(0\)
429.2.bn.b \(112\) \(3.426\) None \(0\) \(14\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)