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Properties

Label 252.8.j
Level $252$
Weight $8$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $84$
Newform subspaces $2$
Sturm bound $384$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(252, [\chi])\).

Total New Old
Modular forms 684 84 600
Cusp forms 660 84 576
Eisenstein series 24 0 24

Trace form

\( 84 q - 142 q^{5} + 2128 q^{9} + O(q^{10}) \) \( 84 q - 142 q^{5} + 2128 q^{9} - 2732 q^{11} + 8518 q^{15} - 23972 q^{17} + 4188 q^{19} + 28126 q^{21} - 86264 q^{23} - 728244 q^{25} - 211680 q^{27} - 90346 q^{29} + 198654 q^{31} + 552404 q^{33} + 343000 q^{35} - 303564 q^{37} - 457604 q^{39} - 102486 q^{41} + 720642 q^{43} - 3843298 q^{45} + 788178 q^{47} - 4941258 q^{49} + 5166818 q^{51} + 5005128 q^{53} + 2699268 q^{55} - 2424450 q^{57} - 2368828 q^{59} - 1728720 q^{63} - 3742002 q^{65} - 771120 q^{67} + 8949104 q^{69} + 3961012 q^{71} - 3202764 q^{73} - 1001354 q^{75} - 3652264 q^{77} - 2735922 q^{79} - 27482612 q^{81} - 2634266 q^{83} + 712254 q^{85} + 29527804 q^{87} + 18111204 q^{89} - 8474844 q^{91} - 8059394 q^{93} - 17675996 q^{95} + 12321348 q^{97} - 78976976 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.8.j.a 252.j 9.c $42$ $78.721$ None 252.8.j.a \(0\) \(-82\) \(-321\) \(-7203\) $\mathrm{SU}(2)[C_{3}]$
252.8.j.b 252.j 9.c $42$ $78.721$ None 252.8.j.b \(0\) \(82\) \(179\) \(7203\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)