Properties

Label 429.1.v
Level $429$
Weight $1$
Character orbit 429.v
Rep. character $\chi_{429}(38,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $3$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 429.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(429, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q - 4q^{4} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{4} - 4q^{9} - 8q^{10} - 8q^{12} + 8q^{16} - 4q^{22} - 4q^{25} + 12q^{30} - 4q^{36} - 4q^{39} - 16q^{40} - 8q^{43} + 12q^{48} - 4q^{49} + 12q^{52} - 4q^{55} + 8q^{64} - 4q^{66} + 12q^{75} - 4q^{81} + 12q^{82} + 12q^{88} + 12q^{90} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(429, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
429.1.v.a \(4\) \(0.214\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-39}) \) None \(-3\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
429.1.v.b \(4\) \(0.214\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-39}) \) None \(3\) \(-1\) \(-2\) \(0\) \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
429.1.v.c \(8\) \(0.214\) \(\Q(\zeta_{20})\) \(D_{10}\) \(\Q(\sqrt{-39}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)