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Properties

Label 252.4.j
Level $252$
Weight $4$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $2$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 300 36 264
Cusp forms 276 36 240
Eisenstein series 24 0 24

Trace form

\( 36 q + 6 q^{3} + 8 q^{5} - 74 q^{9} + O(q^{10}) \) \( 36 q + 6 q^{3} + 8 q^{5} - 74 q^{9} - 98 q^{11} + 208 q^{15} + 76 q^{17} - 180 q^{19} - 56 q^{21} - 284 q^{23} - 594 q^{25} - 900 q^{27} - 676 q^{29} - 36 q^{31} + 446 q^{33} + 280 q^{35} - 144 q^{37} + 508 q^{39} - 246 q^{41} - 342 q^{43} - 1588 q^{45} - 1176 q^{47} - 882 q^{49} + 1850 q^{51} + 1488 q^{53} - 792 q^{55} - 258 q^{57} + 302 q^{59} + 588 q^{63} - 1872 q^{65} - 162 q^{67} + 128 q^{69} + 1984 q^{71} - 828 q^{73} - 2234 q^{75} - 616 q^{77} - 468 q^{79} - 890 q^{81} + 2164 q^{83} - 2016 q^{85} + 3856 q^{87} + 720 q^{89} + 504 q^{91} + 700 q^{93} + 3364 q^{95} + 342 q^{97} + 5956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.4.j.a 252.j 9.c $18$ $14.868$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-5\) \(14\) \(63\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(2-2\beta _{2}+\beta _{12})q^{5}+7\beta _{2}q^{7}+\cdots\)
252.4.j.b 252.j 9.c $18$ $14.868$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(11\) \(-6\) \(-63\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

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