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

• Label: 148.2.k
• Level: $148$
• Weight: $2$
• Character orbit: 148.k
• Rep. character: $\chi_{148}(9,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $24$
• 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.k (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
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	132	24	108
Cusp forms	96	24	72
Eisenstein series	36	0	36

Trace form

24 * q + 3 * q^3 - 3 * q^5 - 9 * q^7 + 3 * q^9 - 6 * q^11 + 9 * q^13 - 3 * q^15 - 3 * q^17 - 12 * q^19 + 12 * q^21 + 18 * q^23 + 15 * q^25 - 6 * q^27 - 3 * q^29 - 48 * q^31 - 27 * q^33 - 42 * q^35 - 24 * q^37 + 36 * q^39 - 6 * q^41 - 24 * q^43 - 69 * q^45 - 3 * q^47 + 39 * q^49 + 3 * q^53 - 9 * q^55 - 69 * q^57 + 6 * q^59 + 60 * q^61 + 42 * q^63 + 30 * q^65 + 30 * q^67 + 39 * q^69 - 15 * q^71 + 18 * q^73 + 150 * q^75 + 90 * q^77 - 12 * q^79 + 48 * q^81 + 21 * q^85 + 138 * q^87 + 24 * q^89 - 27 * q^91 - 54 * q^93 - 81 * q^95 + 18 * q^97 - 69 * 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.k.a	$148$	$2$	148.k	37.f	$9$	$24$	$4$	$1.182$		None		✓	✓	✓	148.2.k.a	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(-9\)		$\mathrm{SU}(2)[C_{9}]$

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

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