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

• Label: 152.2.c
• Level: $152$
• Weight: $2$
• Character orbit: 152.c
• Rep. character: $\chi_{152}(77,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	22	18	4
Cusp forms	18	18	0
Eisenstein series	4	0	4

Trace form

18 * q - 2 * q^2 + 2 * q^4 + 6 * q^6 - 4 * q^7 - 8 * q^8 - 18 * q^9 - 8 * q^10 + 4 * q^12 - 6 * q^16 - 4 * q^17 + 14 * q^18 + 8 * q^20 + 12 * q^22 - 4 * q^23 + 6 * q^24 - 14 * q^25 - 6 * q^26 - 14 * q^28 + 4 * q^30 - 12 * q^32 - 4 * q^34 + 8 * q^36 + 8 * q^39 + 28 * q^40 + 4 * q^41 - 2 * q^42 - 12 * q^44 - 44 * q^46 + 20 * q^47 + 36 * q^48 + 18 * q^49 + 2 * q^50 - 34 * q^54 + 16 * q^55 - 40 * q^56 + 42 * q^58 - 28 * q^60 - 20 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 24 * q^71 + 12 * q^72 - 20 * q^73 + 56 * q^78 - 40 * q^79 + 4 * q^80 + 2 * q^81 + 64 * q^84 + 56 * q^86 - 48 * q^87 + 24 * q^88 - 4 * q^89 + 12 * q^90 + 62 * q^92 - 32 * q^94 + 16 * q^95 - 70 * q^96 + 12 * q^97 - 42 * q^98

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.c.a	$152$	$2$	152.c	8.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-1}) \)	None		✓			152.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-2 i q^{4}+2 q^{7}+(2 i+2)q^{8}+\cdots\)
152.2.c.b	$152$	$2$	152.c	8.b	$2$	$16$	$16$	$1.214$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		152.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)