Properties

Label 252.2.i
Level $252$
Weight $2$
Character orbit 252.i
Rep. character $\chi_{252}(25,\cdot)$
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.i (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

\( 16 q - 4 q^{5} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{5} + q^{7} - 2 q^{9} - 2 q^{11} - q^{13} + 7 q^{15} - 5 q^{17} + 2 q^{19} - 2 q^{21} + 7 q^{23} - 8 q^{25} + 9 q^{27} + 2 q^{29} - 4 q^{31} + 8 q^{33} - 11 q^{35} - q^{37} + 7 q^{39} - 24 q^{41} + 2 q^{43} - 4 q^{45} + 12 q^{47} + 7 q^{49} - 13 q^{51} - 18 q^{53} - 12 q^{55} - 3 q^{57} + 14 q^{59} + 26 q^{61} + 21 q^{63} - 18 q^{65} + 14 q^{67} - 43 q^{69} - 14 q^{71} + 14 q^{73} - 47 q^{75} - 43 q^{77} + 2 q^{79} - 38 q^{81} - 26 q^{83} - 6 q^{85} + 28 q^{87} - 21 q^{89} + 5 q^{91} + 31 q^{93} + 76 q^{95} - q^{97} - 17 q^{99} + O(q^{100}) \)

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.i.a \(2\) \(2.012\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-2\) \(-5\) \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
252.2.i.b \(14\) \(2.012\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(3\) \(-2\) \(6\) \(q+(-\beta _{1}+\beta _{3})q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+\cdots\)

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

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