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Properties

Label 476.3.s
Level $476$
Weight $3$
Character orbit 476.s
Rep. character $\chi_{476}(341,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 476.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(476, [\chi])\).

Total New Old
Modular forms 300 44 256
Cusp forms 276 44 232
Eisenstein series 24 0 24

Trace form

\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + O(q^{10}) \) \( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(476, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
476.3.s.a 476.s 7.d $44$ $12.970$ None 476.3.s.a \(0\) \(-6\) \(0\) \(22\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(476, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(476, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)