Properties

Label 476.1.o
Level $476$
Weight $1$
Character orbit 476.o
Rep. character $\chi_{476}(67,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $3$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 476.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(476, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{21} - 4 q^{25} + 4 q^{26} + 4 q^{33} + 8 q^{36} - 4 q^{42} + 4 q^{53} + 8 q^{64} - 8 q^{66} - 4 q^{68} - 8 q^{69} + 4 q^{72} + 8 q^{77} + 8 q^{84} + 4 q^{93} - 4 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(476, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
476.1.o.a 476.o 476.o $2$ $0.238$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-17}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-q^{7}+\cdots\)
476.1.o.b 476.o 476.o $2$ $0.238$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-17}) \) None \(-1\) \(1\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{7}+\cdots\)
476.1.o.c 476.o 476.o $4$ $0.238$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-17}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots\)