Properties

Label 429.2.bg
Level $429$
Weight $2$
Character orbit 429.bg
Rep. character $\chi_{429}(16,\cdot)$
Character field $\Q(\zeta_{15})$
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.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 224q + 28q^{4} + 28q^{9} + O(q^{10}) \) \( 224q + 28q^{4} + 28q^{9} - 24q^{10} + 4q^{11} - 16q^{12} - 14q^{13} - 24q^{14} - 4q^{15} + 8q^{16} - 16q^{17} - 68q^{20} + 22q^{22} + 12q^{23} - 36q^{24} - 68q^{25} + 56q^{26} - 12q^{28} - 12q^{29} - 4q^{30} + 8q^{31} - 40q^{32} - 2q^{33} + 160q^{34} - 20q^{35} + 28q^{36} + 24q^{37} - 68q^{38} + 8q^{39} - 56q^{40} - 76q^{41} - 12q^{42} - 32q^{43} + 60q^{46} + 68q^{47} - 40q^{48} + 80q^{49} - 20q^{50} - 8q^{51} - 58q^{52} - 100q^{53} + 12q^{55} + 8q^{58} + 2q^{59} - 24q^{60} + 36q^{61} - 16q^{62} - 20q^{65} - 24q^{66} - 88q^{67} - 52q^{68} + 14q^{69} + 128q^{70} - 32q^{71} - 84q^{73} - 68q^{74} - 32q^{75} + 32q^{76} + 116q^{77} - 16q^{78} - 88q^{79} + 64q^{80} + 28q^{81} + 10q^{82} - 16q^{83} + 20q^{85} - 96q^{86} - 112q^{87} - 92q^{88} + 24q^{89} + 8q^{90} - 50q^{91} - 4q^{92} - 8q^{93} + 20q^{94} + 36q^{95} - 156q^{96} + 46q^{97} + 80q^{98} + 12q^{99} + O(q^{100}) \)

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.bg.a \(112\) \(3.426\) None \(0\) \(-14\) \(6\) \(0\)
429.2.bg.b \(112\) \(3.426\) None \(0\) \(14\) \(-6\) \(0\)

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

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