Space of modular forms of level 152, weight 2, and Character 152.i

• Label: 152.2.i
• Level: $152$
• Weight: $2$
• Character orbit: 152.i
• Rep. character: $\chi_{152}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

	Total	New	Old
Modular forms	48	10	38
Cusp forms	32	10	22
Eisenstein series	16	0	16

Trace form

10 * q - 3 * q^3 - 4 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^13 - 4 * q^15 - 8 * q^17 + 9 * q^19 + 6 * q^21 - 6 * q^23 - 9 * q^25 + 18 * q^27 + 4 * q^29 - 24 * q^31 - 5 * q^33 - 12 * q^35 - 16 * q^37 - 8 * q^39 + 15 * q^41 + 10 * q^43 - 8 * q^45 - 6 * q^49 - 20 * q^51 + 16 * q^53 + 14 * q^55 - 38 * q^57 - 25 * q^59 + 12 * q^61 + 40 * q^63 - 4 * q^65 + 5 * q^67 + 20 * q^69 + 8 * q^71 + 29 * q^73 + 6 * q^75 + 20 * q^77 + 6 * q^79 - 25 * q^81 + 46 * q^83 + 6 * q^85 + 64 * q^87 + 12 * q^89 - 44 * q^91 - 36 * q^93 + 42 * q^95 + 11 * q^97 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.2.i.a	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	\(\Q(\sqrt{-3}) \)	None		✓			152.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	\(\Q(\sqrt{-3}) \)	None		✓			152.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c	$152$	$2$	152.i	19.c	$3$	$6$	$3$	$1.214$	6.0.2696112.1	None		✓	✓		152.2.i.c	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(152, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)