Space of modular forms of level 148, weight 2, and Character 148.e

• Label: 148.2.e
• Level: $148$
• Weight: $2$
• Character orbit: 148.e
• Rep. character: $\chi_{148}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	148.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(38\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(148, [\chi])\).

	Total	New	Old
Modular forms	44	6	38
Cusp forms	32	6	26
Eisenstein series	12	0	12

Trace form

6 * q - q^3 + 3 * q^5 - q^7 - 4 * q^9 - 7 * q^13 + q^15 + 3 * q^17 + 7 * q^19 - 9 * q^21 - 8 * q^23 + 12 * q^25 + 14 * q^27 - 4 * q^33 + q^35 + 4 * q^37 - 19 * q^39 - 17 * q^41 - 16 * q^43 - 8 * q^45 - 16 * q^47 - 12 * q^49 + 14 * q^51 - 19 * q^53 + 15 * q^57 + 9 * q^59 + 7 * q^61 + 68 * q^63 + 7 * q^65 - 9 * q^67 - 20 * q^69 + 15 * q^71 + 44 * q^73 - 8 * q^75 + 24 * q^77 + 15 * q^79 + q^81 - 15 * q^83 + 6 * q^85 - 34 * q^87 - 17 * q^89 + 13 * q^91 + 4 * q^93 - 7 * q^95 - 8 * q^97 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(148, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
148.2.e.a	$148$	$2$	148.e	37.c	$3$	$6$	$3$	$1.182$	6.0.27870912.1	None		✓	✓	✓	148.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(148, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)