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Properties

Label 252.9.bc
Level $252$
Weight $9$
Character orbit 252.bc
Rep. character $\chi_{252}(13,\cdot)$
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.bc (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

\( 128 q - 923 q^{7} + 13692 q^{9} + O(q^{10}) \) \( 128 q - 923 q^{7} + 13692 q^{9} + 5694 q^{11} - 47232 q^{15} + 601065 q^{21} - 22794 q^{23} + 5000000 q^{25} - 322140 q^{29} + 8260494 q^{35} - 1093972 q^{37} - 10528470 q^{39} + 2262656 q^{43} - 4003093 q^{49} - 18736026 q^{51} + 84215952 q^{53} + 62335650 q^{57} + 33442485 q^{63} + 30694728 q^{65} - 22149890 q^{67} + 13379628 q^{71} + 27337917 q^{77} - 31159700 q^{79} - 89557056 q^{81} - 28601250 q^{85} - 173131650 q^{91} + 95599596 q^{93} - 150201192 q^{95} + 237300318 q^{99} + O(q^{100}) \)

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

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