Properties

Label 48.3.l
Level $48$
Weight $3$
Character orbit 48.l
Rep. character $\chi_{48}(19,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(48, [\chi])\).

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.3.l.a \(16\) \(1.308\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)