Properties

Label 476.2.i
Level $476$
Weight $2$
Character orbit 476.i
Rep. character $\chi_{476}(137,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $5$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 476.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 156 20 136
Cusp forms 132 20 112
Eisenstein series 24 0 24

Trace form

\( 20 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 12 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 12 q^{9} - 4 q^{11} - 8 q^{15} + 4 q^{17} - 6 q^{19} - 8 q^{21} + 4 q^{23} - 14 q^{25} - 16 q^{27} + 16 q^{29} - 18 q^{31} + 2 q^{33} + 10 q^{35} - 2 q^{37} + 12 q^{39} - 28 q^{41} + 44 q^{43} - 28 q^{45} - 10 q^{47} + 8 q^{49} + 4 q^{53} + 4 q^{55} + 16 q^{57} + 10 q^{59} + 16 q^{61} - 34 q^{63} - 6 q^{65} + 40 q^{69} + 20 q^{71} + 4 q^{73} + 40 q^{75} - 30 q^{77} - 36 q^{79} + 2 q^{81} + 24 q^{83} - 42 q^{87} + 8 q^{89} + 4 q^{91} - 22 q^{93} + 12 q^{95} - 12 q^{97} + 52 q^{99} + O(q^{100}) \)

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.i.a 476.i 7.c $2$ $3.801$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
476.2.i.b 476.i 7.c $2$ $3.801$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
476.2.i.c 476.i 7.c $2$ $3.801$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
476.2.i.d 476.i 7.c $6$ $3.801$ 6.0.1783323.2 None \(0\) \(1\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
476.2.i.e 476.i 7.c $8$ $3.801$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)

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

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