Properties

Label 429.2.f
Level $429$
Weight $2$
Character orbit 429.f
Rep. character $\chi_{429}(131,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 60 48 12
Cusp forms 52 48 4
Eisenstein series 8 0 8

Trace form

\( 48q - 6q^{3} + 48q^{4} + 14q^{9} + O(q^{10}) \) \( 48q - 6q^{3} + 48q^{4} + 14q^{9} - 20q^{12} - 6q^{15} + 8q^{16} - 4q^{22} - 28q^{25} - 12q^{31} + 2q^{33} - 16q^{34} + 26q^{36} + 20q^{37} - 2q^{42} - 50q^{45} - 82q^{48} - 56q^{49} - 20q^{55} - 80q^{58} + 104q^{60} + 16q^{64} - 50q^{66} + 60q^{67} + 6q^{69} + 80q^{70} + 12q^{75} + 10q^{78} + 6q^{81} - 8q^{82} - 52q^{88} - 8q^{91} + 42q^{93} - 92q^{97} + 18q^{99} + O(q^{100}) \)

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.f.a \(48\) \(3.426\) None \(0\) \(-6\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)