Properties

Label 48.4.a
Level $48$
Weight $4$
Character orbit 48.a
Rep. character $\chi_{48}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $32$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 48.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(48))\).

Total New Old
Modular forms 30 3 27
Cusp forms 18 3 15
Eisenstein series 12 0 12

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.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3q - 3q^{3} + 2q^{5} + 32q^{7} + 27q^{9} + O(q^{10}) \) \( 3q - 3q^{3} + 2q^{5} + 32q^{7} + 27q^{9} - 20q^{11} - 46q^{13} + 30q^{15} - 26q^{17} - 12q^{19} - 248q^{23} + 181q^{25} - 27q^{27} - 342q^{29} + 24q^{31} - 12q^{33} + 576q^{35} + 58q^{37} + 366q^{39} + 414q^{41} - 404q^{43} + 18q^{45} - 576q^{47} - 133q^{49} - 678q^{51} + 482q^{53} + 968q^{55} - 84q^{57} + 748q^{59} - 334q^{61} + 288q^{63} - 628q^{65} - 780q^{67} - 264q^{69} - 1288q^{71} - 754q^{73} - 1077q^{75} + 768q^{77} + 40q^{79} + 243q^{81} + 3188q^{83} + 68q^{85} + 1206q^{87} - 66q^{89} - 1088q^{91} + 456q^{93} - 3208q^{95} + 966q^{97} - 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(48))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
48.4.a.a \(1\) \(2.832\) \(\Q\) None \(0\) \(-3\) \(-18\) \(-8\) \(-\) \(+\) \(q-3q^{3}-18q^{5}-8q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
48.4.a.b \(1\) \(2.832\) \(\Q\) None \(0\) \(-3\) \(14\) \(24\) \(+\) \(+\) \(q-3q^{3}+14q^{5}+24q^{7}+9q^{9}+28q^{11}+\cdots\)
48.4.a.c \(1\) \(2.832\) \(\Q\) None \(0\) \(3\) \(6\) \(16\) \(-\) \(-\) \(q+3q^{3}+6q^{5}+2^{4}q^{7}+9q^{9}-12q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(48)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)