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Properties

Label 252.2.j
Level $252$
Weight $2$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{5} + 4 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{5} + 4 q^{9} + 4 q^{11} - 2 q^{15} + 4 q^{17} + 12 q^{19} - 2 q^{21} - 8 q^{23} + 14 q^{29} + 6 q^{31} + 8 q^{33} - 8 q^{35} - 12 q^{37} - 20 q^{39} + 6 q^{41} - 6 q^{43} - 10 q^{45} - 6 q^{47} - 6 q^{49} - 22 q^{51} - 24 q^{53} - 12 q^{55} - 30 q^{57} - 28 q^{59} - 18 q^{65} + 32 q^{69} + 4 q^{71} + 12 q^{73} + 46 q^{75} + 8 q^{77} + 6 q^{79} - 32 q^{81} - 2 q^{83} + 30 q^{85} - 68 q^{87} + 36 q^{89} - 12 q^{91} + 22 q^{93} + 4 q^{95} + 24 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.2.j.a 252.j 9.c $6$ $2.012$ 6.0.309123.1 None \(0\) \(-2\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
252.2.j.b 252.j 9.c $6$ $2.012$ 6.0.309123.1 None \(0\) \(2\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

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