Space of modular forms of level 153, weight 10, and trivial character

• Label: 153.10.a
• Level: $153$
• Weight: $10$
• Character orbit: 153.a
• Rep. character: $\chi_{153}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(153))\).

	Total	New	Old
Modular forms	166	60	106
Cusp forms	158	60	98
Eisenstein series	8	0	8

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

\(3\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	$-$	\(12\)
\(-\)	\(+\)	$-$	\(19\)
\(-\)	\(-\)	$+$	\(17\)
Plus space		\(+\)	\(29\)
Minus space		\(-\)	\(31\)

Trace form

\( 60 q - 34 q^{2} + 15530 q^{4} - 2842 q^{5} + 12050 q^{7} - 43758 q^{8} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(153))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	17
153.10.a.a	$153$	$10$	153.a	1.a	$1$	$5$	$5$	$78.800$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-33\)	\(0\)	\(2018\)	\(874\)		$-$	$-$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{1})q^{2}+(73-20\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
153.10.a.b	$153$	$10$	153.a	1.a	$1$	$5$	$5$	$78.800$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(15\)	\(0\)	\(1732\)	\(-6512\)		$-$	$+$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(259-5\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
153.10.a.c	$153$	$10$	153.a	1.a	$1$	$5$	$5$	$78.800$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(33\)	\(0\)	\(-1480\)	\(-13202\)		$-$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(7-\beta _{1})q^{2}+(177-17\beta _{1}+\beta _{3}-3\beta _{4})q^{4}+\cdots\)
153.10.a.d	$153$	$10$	153.a	1.a	$1$	$7$	$7$	$78.800$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-33\)	\(0\)	\(-2584\)	\(-3130\)		$-$	$-$	$+$	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-5+\beta _{1})q^{2}+(370-7\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
153.10.a.e	$153$	$10$	153.a	1.a	$1$	$7$	$7$	$78.800$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-17\)	\(0\)	\(-1166\)	\(7096\)		$-$	$+$	$-$	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(228+3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
153.10.a.f	$153$	$10$	153.a	1.a	$1$	$7$	$7$	$78.800$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1362\)	\(9388\)		$-$	$+$	$-$	$2^{10}\cdot 3^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(342-3\beta _{1}+\beta _{2})q^{4}+(-198+\cdots)q^{5}+\cdots\)
153.10.a.g	$153$	$10$	153.a	1.a	$1$	$12$	$12$	$78.800$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(0\)	\(-1934\)	\(8768\)		$+$	$+$	$+$	$2^{8}\cdot 3^{12}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(271-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
153.10.a.h	$153$	$10$	153.a	1.a	$1$	$12$	$12$	$78.800$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(0\)	\(1934\)	\(8768\)		$+$	$-$	$-$	$2^{8}\cdot 3^{12}\cdot 7$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(271-2\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(153))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(153)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)