Properties

Label 252.9.z
Level $252$
Weight $9$
Character orbit 252.z
Rep. character $\chi_{252}(73,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $54$
Newform subspaces $5$
Sturm bound $432$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(432\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).

Total New Old
Modular forms 792 54 738
Cusp forms 744 54 690
Eisenstein series 48 0 48

Trace form

\( 54 q - 837 q^{5} - 24 q^{7} + O(q^{10}) \) \( 54 q - 837 q^{5} - 24 q^{7} + 15093 q^{11} + 141453 q^{17} + 200133 q^{19} - 458433 q^{23} + 2182812 q^{25} + 110484 q^{29} - 1067031 q^{31} + 4086531 q^{35} + 2190879 q^{37} + 311880 q^{43} - 12493629 q^{47} - 6375252 q^{49} + 5668515 q^{53} + 11166309 q^{59} - 51201405 q^{61} - 11539422 q^{65} - 3651657 q^{67} - 51102792 q^{71} + 23677065 q^{73} - 51320493 q^{77} - 54023409 q^{79} - 78211362 q^{85} + 91157805 q^{89} - 797646 q^{91} + 15128343 q^{95} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.9.z.a $2$ $102.659$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4273\) \(q+(1504+1265\zeta_{6})q^{7}+(-5055+10110\zeta_{6})q^{13}+\cdots\)
252.9.z.b $10$ $102.659$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-1389\) \(1217\) \(q+(-92-93\beta _{1}-\beta _{5})q^{5}+(139-35\beta _{1}+\cdots)q^{7}+\cdots\)
252.9.z.c $10$ $102.659$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(837\) \(1526\) \(q+(112+56\beta _{1}-\beta _{3})q^{5}+(178+50\beta _{1}+\cdots)q^{7}+\cdots\)
252.9.z.d $12$ $102.659$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-285\) \(198\) \(q+(-2^{4}-2^{4}\beta _{1}+\beta _{3})q^{5}+(114-14^{2}\beta _{1}+\cdots)q^{7}+\cdots\)
252.9.z.e $20$ $102.659$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-7238\) \(q+(-\beta _{1}-\beta _{4})q^{5}+(-577-430\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)