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

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

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.k.a \(2\) \(2.012\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(1\) \(q+(-2+2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
252.2.k.b \(2\) \(2.012\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(3-\zeta_{6})q^{7}+5q^{13}+(1-\zeta_{6})q^{19}+\cdots\)
252.2.k.c \(2\) \(2.012\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-4\) \(q+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)

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

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