Properties

Label 48.4.k
Level $48$
Weight $4$
Character orbit 48.k
Rep. character $\chi_{48}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44q - 2q^{3} - 4q^{4} + 28q^{6} - 8q^{7} + O(q^{10}) \) \( 44q - 2q^{3} - 4q^{4} + 28q^{6} - 8q^{7} + 56q^{10} - 80q^{12} - 4q^{13} - 112q^{16} + 52q^{18} + 20q^{19} - 56q^{21} - 40q^{22} - 120q^{24} - 134q^{27} - 296q^{28} - 332q^{30} - 4q^{33} + 520q^{34} - 604q^{36} - 4q^{37} + 596q^{39} + 632q^{40} + 696q^{42} - 436q^{43} - 252q^{45} + 664q^{46} + 1200q^{48} + 972q^{49} - 648q^{51} + 320q^{52} + 1592q^{54} + 280q^{55} - 424q^{58} + 800q^{60} - 916q^{61} - 2056q^{64} - 668q^{66} - 1636q^{67} + 52q^{69} - 5192q^{70} - 3704q^{72} + 1454q^{75} - 568q^{76} - 4932q^{78} - 4q^{81} + 768q^{82} - 2096q^{84} + 736q^{85} + 1284q^{87} + 8864q^{88} + 2672q^{90} + 424q^{91} - 2084q^{93} + 5616q^{94} + 8008q^{96} - 8q^{97} + 1196q^{99} + O(q^{100}) \)

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.k.a \(44\) \(2.832\) None \(0\) \(-2\) \(0\) \(-8\)