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Properties

Label 252.8.i
Level $252$
Weight $8$
Character orbit 252.i
Rep. character $\chi_{252}(25,\cdot)$
Character field $\Q(\zeta_{3})$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 112 q + 500 q^{5} - 83 q^{7} + 934 q^{9} + O(q^{10}) \) \( 112 q + 500 q^{5} - 83 q^{7} + 934 q^{9} - 2954 q^{11} + 1847 q^{13} + 11659 q^{15} + 52915 q^{17} - 22342 q^{19} - 24362 q^{21} + 22291 q^{23} - 875000 q^{25} - 159507 q^{27} - 174274 q^{29} - 107524 q^{31} - 9736 q^{33} - 933671 q^{35} - 6217 q^{37} - 1482389 q^{39} + 1258716 q^{41} + 24026 q^{43} - 2348896 q^{45} + 1385004 q^{47} + 471667 q^{49} + 3789071 q^{51} + 904806 q^{53} + 1177332 q^{55} + 194469 q^{57} - 4523386 q^{59} - 292462 q^{61} - 29967 q^{63} + 368046 q^{65} + 2503718 q^{67} - 9544963 q^{69} + 4196650 q^{71} + 5865902 q^{73} + 4525957 q^{75} + 1170749 q^{77} - 6139318 q^{79} + 1860874 q^{81} - 1327058 q^{83} - 1317750 q^{85} - 9570764 q^{87} + 10221855 q^{89} + 4729625 q^{91} - 5442977 q^{93} + 37968268 q^{95} - 3307417 q^{97} - 16542485 q^{99} + O(q^{100}) \)

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

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