Properties

Label 48.4.j
Level $48$
Weight $4$
Character orbit 48.j
Rep. character $\chi_{48}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(48, [\chi])\).

Total New Old
Modular forms 52 24 28
Cusp forms 44 24 20
Eisenstein series 8 0 8

Trace form

\( 24q - 20q^{4} + 84q^{8} + O(q^{10}) \) \( 24q - 20q^{4} + 84q^{8} + 72q^{10} - 40q^{11} - 24q^{12} - 348q^{14} + 120q^{15} - 192q^{16} - 36q^{18} + 24q^{19} + 80q^{20} + 704q^{22} + 228q^{24} - 20q^{26} - 344q^{28} + 400q^{29} - 408q^{30} - 744q^{31} - 960q^{32} - 704q^{34} - 456q^{35} + 108q^{36} + 16q^{37} + 1256q^{38} + 1744q^{40} + 660q^{42} + 1240q^{43} - 200q^{44} - 1432q^{46} - 528q^{48} - 1176q^{49} + 708q^{50} + 744q^{51} + 1008q^{52} + 752q^{53} + 108q^{54} + 1344q^{56} + 1936q^{58} - 1376q^{59} - 1224q^{60} - 912q^{61} - 996q^{62} - 504q^{63} - 56q^{64} + 976q^{65} - 1368q^{66} - 2256q^{67} - 1568q^{68} - 528q^{69} - 1760q^{70} - 612q^{72} - 2740q^{74} + 1104q^{75} - 1880q^{76} + 1904q^{77} + 1692q^{78} + 5992q^{79} + 712q^{80} - 1944q^{81} - 40q^{82} + 2680q^{83} + 1800q^{84} - 240q^{85} - 1712q^{86} - 3936q^{88} + 648q^{90} - 3496q^{91} + 5296q^{92} + 5272q^{94} - 7728q^{95} + 2880q^{96} + 6760q^{98} - 360q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.4.j.a \(24\) \(2.832\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)