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Properties

Label 48.6.j
Level $48$
Weight $6$
Character orbit 48.j
Rep. character $\chi_{48}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(48, [\chi])\).

Total New Old
Modular forms 84 40 44
Cusp forms 76 40 36
Eisenstein series 8 0 8

Trace form

\( 40 q + 44 q^{4} - 492 q^{8} + O(q^{10}) \) \( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.6.j.a 48.j 16.e $40$ $7.698$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)