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Properties

Label 252.9.p
Level $252$
Weight $9$
Character orbit 252.p
Rep. character $\chi_{252}(61,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 780 128 652
Cusp forms 756 128 628
Eisenstein series 24 0 24

Trace form

\( 128 q - 923 q^{7} - 6846 q^{9} + O(q^{10}) \) \( 128 q - 923 q^{7} - 6846 q^{9} - 11388 q^{11} + 5055 q^{13} - 149283 q^{15} + 31725 q^{17} - 365940 q^{21} + 666966 q^{23} - 10000000 q^{25} - 2680785 q^{27} - 1270956 q^{29} + 214176 q^{31} + 2413233 q^{33} + 621321 q^{35} - 273493 q^{37} - 3829809 q^{39} + 1607166 q^{41} - 1131328 q^{43} - 7110141 q^{45} + 6602256 q^{47} + 7344395 q^{49} - 11484963 q^{51} + 14434902 q^{53} - 31372005 q^{57} - 24127695 q^{59} - 15766797 q^{61} + 43758195 q^{63} - 16499265 q^{65} + 11074945 q^{67} - 38525655 q^{69} - 93404814 q^{71} + 40343745 q^{75} + 123041397 q^{77} + 32771821 q^{79} - 74522358 q^{81} + 210547890 q^{83} - 28601250 q^{85} + 3963471 q^{87} + 166263039 q^{89} + 86565825 q^{91} + 94467279 q^{93} - 18035544 q^{95} - 86346849 q^{97} + 376350687 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)