Properties

Label 48.3.i
Level $48$
Weight $3$
Character orbit 48.i
Rep. character $\chi_{48}(5,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

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

Trace form

\( 28q - 2q^{3} - 4q^{4} + 4q^{6} + O(q^{10}) \) \( 28q - 2q^{3} - 4q^{4} + 4q^{6} - 24q^{10} - 32q^{12} - 4q^{13} - 4q^{15} - 16q^{16} - 60q^{18} - 36q^{19} + 16q^{21} + 40q^{22} - 56q^{24} - 50q^{27} + 120q^{28} + 84q^{30} - 8q^{31} - 4q^{33} + 136q^{34} + 196q^{36} - 4q^{37} + 88q^{40} + 280q^{42} - 68q^{43} - 52q^{45} - 200q^{46} + 112q^{48} - 36q^{49} + 96q^{51} - 320q^{52} - 128q^{54} - 568q^{58} - 576q^{60} - 36q^{61} + 192q^{63} - 232q^{64} - 572q^{66} + 124q^{67} - 20q^{69} + 312q^{70} - 312q^{72} + 178q^{75} + 776q^{76} + 236q^{78} + 248q^{79} - 4q^{81} + 736q^{82} + 880q^{84} - 64q^{85} + 352q^{88} + 1008q^{90} + 288q^{91} - 68q^{93} - 336q^{94} + 488q^{96} - 8q^{97} - 292q^{99} + O(q^{100}) \)

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.i.a \(8\) \(1.308\) 8.0.629407744.1 None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
48.3.i.b \(20\) \(1.308\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)