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

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

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.e.a 429.e 429.e $8$ $3.426$ 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
429.2.e.b 429.e 429.e $8$ $3.426$ 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{4}q^{6}+\cdots\)
429.2.e.c 429.e 429.e $16$ $3.426$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
429.2.e.d 429.e 429.e $20$ $3.426$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-143}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-2+\beta _{8})q^{4}+\beta _{7}q^{6}+\cdots\)