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 $1$

Related objects

Downloads

Learn more

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

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

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 \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)