Space of modular forms of level 152, weight 2, and trivial character

• Label: 152.2.a
• Level: $152$
• Weight: $2$
• Character orbit: 152.a
• Rep. character: $\chi_{152}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(152))\).

	Total	New	Old
Modular forms	24	5	19
Cusp forms	17	5	12
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(3\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(4\)

Trace form

5 * q + 4 * q^7 + 11 * q^9 - 6 * q^11 + 2 * q^13 - 8 * q^15 + 2 * q^17 - 3 * q^19 - 6 * q^23 - 3 * q^25 - 10 * q^29 + 12 * q^31 - 4 * q^33 - 6 * q^35 - 14 * q^37 - 10 * q^39 + 6 * q^41 + 2 * q^43 - 28 * q^45 - 18 * q^47 + 9 * q^49 - 4 * q^51 + 2 * q^53 + 22 * q^55 + 2 * q^57 - 8 * q^59 + 12 * q^61 + 38 * q^63 + 16 * q^65 + 28 * q^67 - 44 * q^69 - 8 * q^71 - 2 * q^73 + 36 * q^75 - 2 * q^77 + 12 * q^79 + 37 * q^81 + 8 * q^83 + 6 * q^85 - 10 * q^87 + 6 * q^89 + 32 * q^91 - 12 * q^93 + 22 * q^97 - 58 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(152))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	19
152.2.a.a	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	\(\Q\)	None	✓	✓	✓	✓	152.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	\(\Q\)	None	✓	✓	✓	✓	152.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c	$152$	$2$	152.a	1.a	$1$	$3$	$3$	$1.214$	3.3.961.1	None	✓	✓	✓	✓	152.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(152)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)