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Properties

Label 252.8.bm
Level $252$
Weight $8$
Character orbit 252.bm
Rep. character $\chi_{252}(173,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(252, [\chi])\).

Total New Old
Modular forms 684 112 572
Cusp forms 660 112 548
Eisenstein series 24 0 24

Trace form

\( 112 q + 83 q^{7} + 180 q^{9} + O(q^{10}) \) \( 112 q + 83 q^{7} + 180 q^{9} - 5541 q^{13} - 15159 q^{15} - 40833 q^{17} - 55188 q^{21} + 1750000 q^{25} + 265347 q^{27} + 96018 q^{29} + 161286 q^{31} + 820989 q^{33} + 147435 q^{35} + 6217 q^{37} - 81039 q^{39} + 711402 q^{41} - 24026 q^{43} + 2049501 q^{45} - 2077506 q^{47} + 797005 q^{49} - 53589 q^{51} - 2556360 q^{53} - 2359065 q^{57} + 608565 q^{59} - 8169585 q^{61} - 1088397 q^{63} - 3847431 q^{65} - 1251859 q^{67} - 3898461 q^{69} + 9025365 q^{75} + 8459595 q^{77} - 6020917 q^{79} + 90828 q^{81} + 1317750 q^{85} + 4294329 q^{87} + 14381367 q^{89} + 427149 q^{91} - 4830117 q^{93} - 11165466 q^{95} + 9922251 q^{97} + 11232531 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)