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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
429.2.s.a 429.s 13.e $24$ $3.426$ None \(0\) \(12\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$
429.2.s.b 429.s 13.e $28$ $3.426$ None \(0\) \(-14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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