Properties

Label 252.2.l
Level $252$
Weight $2$
Character orbit 252.l
Rep. character $\chi_{252}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
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 16 92
Cusp forms 84 16 68
Eisenstein series 24 0 24

Trace form

\( 16q + 8q^{5} + q^{7} + 4q^{9} + O(q^{10}) \) \( 16q + 8q^{5} + q^{7} + 4q^{9} + 4q^{11} - q^{13} + 7q^{15} - 5q^{17} + 2q^{19} + 4q^{21} - 14q^{23} + 16q^{25} + 9q^{27} + 2q^{29} + 2q^{31} + 5q^{33} - 11q^{35} - q^{37} - 29q^{39} - 24q^{41} + 2q^{43} - 7q^{45} - 6q^{47} - 11q^{49} - q^{51} - 18q^{53} - 12q^{55} - 3q^{57} - 7q^{59} - 13q^{61} - 51q^{63} + 9q^{65} - 7q^{67} - 43q^{69} - 14q^{71} + 14q^{73} + q^{75} + 35q^{77} - q^{79} + 40q^{81} - 26q^{83} - 6q^{85} - 5q^{87} - 21q^{89} + 5q^{91} + 7q^{93} - 38q^{95} - q^{97} - 17q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.l.a \(2\) \(2.012\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(4\) \(q+(1-2\zeta_{6})q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
252.2.l.b \(14\) \(2.012\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(4\) \(-3\) \(q+\beta _{1}q^{3}+(-\beta _{5}+\beta _{9})q^{5}+\beta _{6}q^{7}+\cdots\)

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

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