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Properties

Label 48.8.j
Level $48$
Weight $8$
Character orbit 48.j
Rep. character $\chi_{48}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 48.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(48, [\chi])\).

Total New Old
Modular forms 116 56 60
Cusp forms 108 56 52
Eisenstein series 8 0 8

Trace form

\( 56 q + 364 q^{4} + 2004 q^{8} + O(q^{10}) \) \( 56 q + 364 q^{4} + 2004 q^{8} - 19448 q^{10} - 2408 q^{11} + 15336 q^{12} - 44028 q^{14} + 27000 q^{15} + 2496 q^{16} + 20412 q^{18} - 60584 q^{19} + 82000 q^{20} + 112960 q^{22} + 40932 q^{24} + 363980 q^{26} - 89816 q^{28} + 103376 q^{29} + 338472 q^{30} - 714984 q^{31} - 571200 q^{32} - 824128 q^{34} + 816504 q^{35} - 37908 q^{36} - 831152 q^{37} + 1921576 q^{38} + 450384 q^{40} - 97740 q^{42} - 386664 q^{43} + 1417400 q^{44} - 787672 q^{46} + 544752 q^{48} - 6588344 q^{49} + 2069988 q^{50} - 1496664 q^{51} - 141712 q^{52} - 1815632 q^{53} + 78732 q^{54} + 9766848 q^{56} - 1661168 q^{58} + 1835936 q^{59} - 1084104 q^{60} - 2279888 q^{61} - 14719044 q^{62} - 2000376 q^{63} - 4704440 q^{64} + 2853776 q^{65} - 1878552 q^{66} + 9576368 q^{67} + 9981536 q^{68} + 4790448 q^{69} + 23508640 q^{70} + 836892 q^{72} + 18583468 q^{74} - 5630256 q^{75} - 9326552 q^{76} - 11914448 q^{77} - 18289476 q^{78} + 19459688 q^{79} - 26364088 q^{80} - 29760696 q^{81} - 25490920 q^{82} + 503480 q^{83} + 5879304 q^{84} - 7534000 q^{85} + 32307920 q^{86} + 71877536 q^{88} + 2618568 q^{90} - 177640 q^{91} - 16335952 q^{92} - 110051624 q^{94} + 64673232 q^{95} - 46578240 q^{96} - 8969560 q^{98} - 1755432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.8.j.a 48.j 16.e $56$ $14.994$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{8}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)