Space of modular forms of level 48, weight 3, and Character 48.e

• Label: 48.3.e
• Level: $48$
• Weight: $3$
• Character orbit: 48.e
• Rep. character: $\chi_{48}(17,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	22	5	17
Cusp forms	10	3	7
Eisenstein series	12	2	10

Trace form

3 * q + q^3 + 10 * q^7 - 5 * q^9 - 2 * q^13 - 32 * q^15 - 30 * q^19 - 18 * q^21 + 11 * q^25 + 73 * q^27 + 90 * q^31 + 32 * q^33 + 14 * q^37 - 86 * q^39 - 142 * q^43 + 64 * q^45 - 71 * q^49 + 128 * q^51 + 64 * q^55 - 74 * q^57 - 98 * q^61 - 102 * q^63 - 126 * q^67 - 64 * q^69 + 118 * q^73 + 89 * q^75 + 122 * q^79 + 115 * q^81 + 256 * q^85 - 96 * q^87 + 164 * q^91 + 94 * q^93 - 186 * q^97 - 64 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.3.e.a	$48$	$3$	48.e	3.b	$2$	$1$	$1$	$1.308$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				12.3.c.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}-2q^{7}+9q^{9}-22q^{13}-26q^{19}+\cdots\)
48.3.e.b	$48$	$3$	48.e	3.b	$2$	$2$	$2$	$1.308$	\(\Q(\sqrt{-2}) \)	None			✓		24.3.e.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+\cdots)q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(48, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)