Properties

Label 48.4.c
Level $48$
Weight $4$
Character orbit 48.c
Rep. character $\chi_{48}(47,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 48.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(48, [\chi])\).

Total New Old
Modular forms 30 6 24
Cusp forms 18 6 12
Eisenstein series 12 0 12

Trace form

\( 6 q + 30 q^{9} + O(q^{10}) \) \( 6 q + 30 q^{9} + 36 q^{13} - 204 q^{21} - 402 q^{25} + 576 q^{33} + 1044 q^{37} - 1152 q^{45} - 1086 q^{49} + 2364 q^{57} + 1476 q^{61} - 3456 q^{69} - 4068 q^{73} + 2070 q^{81} + 4608 q^{85} - 1404 q^{93} - 1620 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.4.c.a 48.c 12.b $2$ $2.832$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-6\zeta_{6}q^{7}-3^{3}q^{9}+70q^{13}+\cdots\)
48.4.c.b 48.c 12.b $4$ $2.832$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(48, [\chi]) \cong \)