Properties

Label 429.2.e
Level $429$
Weight $2$
Character orbit 429.e
Rep. character $\chi_{429}(428,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $4$
Sturm bound $112$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(4\)
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 60 0
Cusp forms 52 52 0
Eisenstein series 8 8 0

Trace form

\( 52q - 4q^{3} - 56q^{4} - 12q^{9} + O(q^{10}) \) \( 52q - 4q^{3} - 56q^{4} - 12q^{9} - 8q^{12} + 56q^{16} - 12q^{22} + 20q^{25} - 16q^{27} - 22q^{36} - 2q^{42} - 10q^{48} + 12q^{49} + 8q^{55} - 112q^{64} - 18q^{66} - 36q^{69} - 72q^{75} + 62q^{78} + 52q^{81} + 40q^{82} + 28q^{88} + 48q^{91} + O(q^{100}) \)

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.e.a \(8\) \(3.426\) 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
429.2.e.b \(8\) \(3.426\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{4}q^{6}+\cdots\)
429.2.e.c \(16\) \(3.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
429.2.e.d \(20\) \(3.426\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-143}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-2+\beta _{8})q^{4}+\beta _{7}q^{6}+\cdots\)