Properties

Label 48.3.g
Level $48$
Weight $3$
Character orbit 48.g
Rep. character $\chi_{48}(31,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

Trace form

\( 2q + 12q^{5} - 6q^{9} + O(q^{10}) \) \( 2q + 12q^{5} - 6q^{9} - 28q^{13} - 12q^{17} - 24q^{21} + 22q^{25} + 60q^{29} + 72q^{33} + 52q^{37} - 108q^{41} - 36q^{45} + 2q^{49} - 36q^{53} + 24q^{57} - 140q^{61} - 168q^{65} + 164q^{73} + 288q^{77} + 18q^{81} - 72q^{85} + 228q^{89} - 72q^{93} + 68q^{97} + O(q^{100}) \)

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.g.a \(2\) \(1.308\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(12\) \(0\) \(q-\zeta_{6}q^{3}+6q^{5}-4\zeta_{6}q^{7}-3q^{9}+12\zeta_{6}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)