Properties

Label 476.2.b
Level $476$
Weight $2$
Character orbit 476.b
Rep. character $\chi_{476}(169,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 476.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(476, [\chi])\).

Total New Old
Modular forms 78 8 70
Cusp forms 66 8 58
Eisenstein series 12 0 12

Trace form

\( 8 q - 12 q^{9} + O(q^{10}) \) \( 8 q - 12 q^{9} + 20 q^{13} + 12 q^{19} - 8 q^{21} - 12 q^{25} - 4 q^{33} - 4 q^{35} - 12 q^{43} + 24 q^{47} - 8 q^{49} - 20 q^{51} + 20 q^{53} - 4 q^{55} - 24 q^{59} - 4 q^{67} + 44 q^{69} + 16 q^{77} + 16 q^{81} + 4 q^{83} - 44 q^{85} + 52 q^{87} - 16 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(476, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
476.2.b.a 476.b 17.b $8$ $3.801$ 8.0.980441344.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}+\beta _{7})q^{3}+\beta _{3}q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)