Properties

Label 429.2.b
Level $429$
Weight $2$
Character orbit 429.b
Rep. character $\chi_{429}(298,\cdot)$
Character field $\Q$
Dimension $24$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 60 24 36
Cusp forms 52 24 28
Eisenstein series 8 0 8

Trace form

\( 24q + 4q^{3} - 24q^{4} + 24q^{9} + O(q^{10}) \) \( 24q + 4q^{3} - 24q^{4} + 24q^{9} - 12q^{12} + 12q^{13} - 16q^{14} + 40q^{16} + 24q^{17} + 4q^{22} - 40q^{25} - 8q^{26} + 4q^{27} - 16q^{29} - 8q^{35} - 24q^{36} - 32q^{38} - 12q^{39} - 40q^{40} + 48q^{42} + 8q^{43} + 28q^{48} - 72q^{49} - 16q^{51} - 44q^{52} + 16q^{53} + 16q^{55} - 16q^{56} + 16q^{61} + 96q^{62} - 8q^{64} + 40q^{65} + 8q^{66} - 32q^{68} - 16q^{69} + 24q^{74} - 12q^{75} - 4q^{78} + 48q^{79} + 24q^{81} - 32q^{87} - 36q^{88} - 8q^{91} - 32q^{92} + 32q^{94} + 8q^{95} + O(q^{100}) \)

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.b.a \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
429.2.b.b \(14\) \(3.426\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(14\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-1-\beta _{5}+\beta _{6})q^{4}+\cdots\)

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

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