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Properties

Label 252.2.k
Level $252$
Weight $2$
Character orbit 252.k
Rep. character $\chi_{252}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $3$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 120 6 114
Cusp forms 72 6 66
Eisenstein series 48 0 48

Trace form

\( 6 q + q^{5} + 2 q^{7} + O(q^{10}) \) \( 6 q + q^{5} + 2 q^{7} - q^{11} + 8 q^{13} + 11 q^{17} + 3 q^{19} + 11 q^{23} + 2 q^{25} + 4 q^{29} - 7 q^{31} - 25 q^{35} - 9 q^{37} - 24 q^{41} - 12 q^{43} - 3 q^{47} - 9 q^{53} - 26 q^{55} + 13 q^{59} - 7 q^{61} + 12 q^{65} - 11 q^{67} + 20 q^{71} - 5 q^{73} - 11 q^{77} - q^{79} - 28 q^{83} - 14 q^{85} + 15 q^{89} + 14 q^{91} - q^{95} + 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.2.k.a 252.k 7.c $2$ $2.012$ \(\Q(\sqrt{-3}) \) None 84.2.i.a \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
252.2.k.b 252.k 7.c $2$ $2.012$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 252.2.k.b \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{3}]$ \(q+(3-\zeta_{6})q^{7}+5q^{13}+(1-\zeta_{6})q^{19}+\cdots\)
252.2.k.c 252.k 7.c $2$ $2.012$ \(\Q(\sqrt{-3}) \) None 28.2.e.a \(0\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)