Properties

Label 429.2.s
Level $429$
Weight $2$
Character orbit 429.s
Rep. character $\chi_{429}(166,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $52$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 120 52 68
Cusp forms 104 52 52
Eisenstein series 16 0 16

Trace form

\( 52q - 2q^{3} + 32q^{4} + 6q^{7} - 26q^{9} + O(q^{10}) \) \( 52q - 2q^{3} + 32q^{4} + 6q^{7} - 26q^{9} - 8q^{12} - 10q^{13} + 16q^{14} - 36q^{16} + 12q^{17} + 12q^{19} - 4q^{22} - 12q^{23} - 36q^{25} - 52q^{26} + 4q^{27} - 48q^{28} + 4q^{29} + 8q^{35} + 32q^{36} + 32q^{38} + 4q^{39} + 40q^{40} - 12q^{41} + 12q^{42} - 6q^{43} - 12q^{45} + 24q^{46} - 8q^{48} + 28q^{49} - 60q^{50} + 16q^{51} + 12q^{52} - 40q^{53} - 16q^{55} + 16q^{56} + 48q^{59} - 6q^{61} + 12q^{62} - 6q^{63} - 80q^{64} - 4q^{65} + 16q^{66} - 30q^{67} - 40q^{68} + 16q^{69} - 12q^{71} + 48q^{74} + 22q^{75} + 48q^{76} - 20q^{78} - 68q^{79} + 96q^{80} - 26q^{81} + 36q^{82} - 12q^{84} - 60q^{85} - 4q^{87} + 12q^{89} + 26q^{91} + 80q^{92} + 18q^{93} + 28q^{94} - 56q^{95} - 30q^{97} - 96q^{98} + O(q^{100}) \)

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.s.a \(24\) \(3.426\) None \(0\) \(12\) \(0\) \(6\)
429.2.s.b \(28\) \(3.426\) None \(0\) \(-14\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)