Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(48))\).

Total New Old
Modular forms 14 1 13
Cusp forms 3 1 2
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + q^{3} - 2q^{5} + q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} + 2q^{17} + 4q^{19} + 8q^{23} - q^{25} + q^{27} + 6q^{29} - 8q^{31} - 4q^{33} + 6q^{37} - 2q^{39} - 6q^{41} - 4q^{43} - 2q^{45} - 7q^{49} + 2q^{51} - 2q^{53} + 8q^{55} + 4q^{57} - 4q^{59} - 2q^{61} + 4q^{65} + 4q^{67} + 8q^{69} - 8q^{71} + 10q^{73} - q^{75} + 8q^{79} + q^{81} + 4q^{83} - 4q^{85} + 6q^{87} - 6q^{89} - 8q^{93} - 8q^{95} + 2q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(48))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
48.2.a.a \(1\) \(0.383\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(48)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)