↑

Properties

Label 48.2.k
Level $48$
Weight $2$
Character orbit 48.k
Rep. character $\chi_{48}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(48, [\chi])\).

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

Trace form

\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} + O(q^{10}) \) \( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.2.k.a 48.k 48.k $12$ $0.383$ 12.0.\(\cdots\).2 None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}-\beta _{10}q^{3}+(-\beta _{1}+\beta _{10}+\beta _{11})q^{4}+\cdots\)