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Properties

Label 252.9.v
Level $252$
Weight $9$
Character orbit 252.v
Rep. character $\chi_{252}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
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 776 576 200
Cusp forms 760 576 184
Eisenstein series 16 0 16

Trace form

\( 576 q - 3234 q^{6} + 19908 q^{8} + 3808 q^{9} + O(q^{10}) \) \( 576 q - 3234 q^{6} + 19908 q^{8} + 3808 q^{9} - 17220 q^{12} - 55104 q^{17} + 826994 q^{18} + 209622 q^{20} - 208166 q^{24} - 22500000 q^{25} + 5252520 q^{26} - 6021752 q^{30} + 1612050 q^{32} - 6873440 q^{33} - 1750308 q^{34} + 3796544 q^{36} - 3607380 q^{38} - 577500 q^{40} - 6877920 q^{41} + 11284700 q^{42} + 15414336 q^{44} - 13812288 q^{45} + 17214792 q^{46} + 3786188 q^{48} + 237180384 q^{49} - 7423158 q^{50} - 9642654 q^{52} - 14474880 q^{53} + 1551914 q^{54} - 9861664 q^{57} + 12719070 q^{58} + 13434836 q^{60} + 68929560 q^{62} + 23792244 q^{64} + 1741632 q^{65} + 172103862 q^{66} - 92016834 q^{68} + 73671360 q^{69} + 76770986 q^{72} + 64792896 q^{73} - 130080132 q^{74} + 29869476 q^{76} + 276194548 q^{78} + 292073880 q^{80} - 21878560 q^{81} - 197507772 q^{82} - 571438 q^{84} + 182025618 q^{86} + 63575400 q^{88} + 230170752 q^{89} + 251730752 q^{90} + 109239186 q^{92} - 392082432 q^{93} - 250990026 q^{94} + 189443464 q^{96} + 112596960 q^{97} + O(q^{100}) \)

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

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)