Properties

Label 252.9.bh
Level $252$
Weight $9$
Character orbit 252.bh
Rep. character $\chi_{252}(137,\cdot)$
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.bh (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

\( 128 q + 923 q^{7} - 9374 q^{9} + O(q^{10}) \) \( 128 q + 923 q^{7} - 9374 q^{9} + 17082 q^{11} - 1685 q^{13} + 106783 q^{15} - 31725 q^{17} + 92554 q^{19} - 560708 q^{21} - 1000449 q^{23} + 5000000 q^{25} + 1194525 q^{27} + 948816 q^{29} - 142784 q^{31} + 296468 q^{33} - 3488895 q^{35} + 273493 q^{37} - 107801 q^{39} + 2151648 q^{41} + 1131328 q^{43} - 11444734 q^{45} + 3561899 q^{49} - 10625137 q^{51} + 36078300 q^{53} + 13193184 q^{55} - 34145295 q^{57} + 34901410 q^{61} + 592101 q^{63} - 22149890 q^{67} - 104117929 q^{69} - 11872994 q^{73} - 80761361 q^{75} + 143491689 q^{77} + 107224174 q^{79} + 49223134 q^{81} + 28601250 q^{85} + 257943082 q^{87} - 122074911 q^{89} + 34062529 q^{91} - 217774979 q^{93} + 28782283 q^{97} - 141254777 q^{99} + O(q^{100}) \)

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

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