Space of modular forms of level 154, weight 6, and trivial character

• Label: 154.6.a
• Level: $154$
• Weight: $6$
• Character orbit: 154.a
• Rep. character: $\chi_{154}(1,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $10$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	154.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(154))\).

	Total	New	Old
Modular forms	124	26	98
Cusp forms	116	26	90
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.

\(2\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(11\)
Minus space			\(-\)	\(15\)

Trace form

\( 26 q - 8 q^{2} + 4 q^{3} + 416 q^{4} - 72 q^{5} - 128 q^{8} + 2554 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(154))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	11
154.6.a.a	$154$	$6$	154.a	1.a	$1$	$1$	$1$	$24.699$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(-30\)	\(42\)	\(49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-30q^{3}+2^{4}q^{4}+42q^{5}+120q^{6}+\cdots\)
154.6.a.b	$154$	$6$	154.a	1.a	$1$	$1$	$1$	$24.699$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(-20\)	\(6\)	\(49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-20q^{3}+2^{4}q^{4}+6q^{5}-80q^{6}+\cdots\)
154.6.a.c	$154$	$6$	154.a	1.a	$1$	$1$	$1$	$24.699$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(5\)	\(-49\)	\(49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+5q^{3}+2^{4}q^{4}-7^{2}q^{5}+20q^{6}+\cdots\)
154.6.a.d	$154$	$6$	154.a	1.a	$1$	$2$	$2$	$24.699$	\(\Q(\sqrt{113}) \)	None	✓	$1$	$0$	\(-8\)	\(15\)	\(-47\)	\(98\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+(9-3\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
154.6.a.e	$154$	$6$	154.a	1.a	$1$	$2$	$2$	$24.699$	\(\Q(\sqrt{337}) \)	None	✓	$1$	$1$	\(8\)	\(7\)	\(-63\)	\(-98\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(4-\beta )q^{3}+2^{4}q^{4}+(-34+\cdots)q^{5}+\cdots\)
154.6.a.f	$154$	$6$	154.a	1.a	$1$	$3$	$3$	$24.699$	3.3.682584.1	None	✓	$1$	$1$	\(-12\)	\(7\)	\(-137\)	\(147\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+(2+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
154.6.a.g	$154$	$6$	154.a	1.a	$1$	$3$	$3$	$24.699$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(-15\)	\(119\)	\(-147\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(-5+\beta _{1})q^{3}+2^{4}q^{4}+(40+\cdots)q^{5}+\cdots\)
154.6.a.h	$154$	$6$	154.a	1.a	$1$	$4$	$4$	$24.699$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-16\)	\(-15\)	\(7\)	\(-196\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-4+\beta _{1})q^{3}+2^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)
154.6.a.i	$154$	$6$	154.a	1.a	$1$	$4$	$4$	$24.699$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-16\)	\(25\)	\(25\)	\(-196\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-4q^{2}+(6+\beta _{1})q^{3}+2^{4}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots\)
154.6.a.j	$154$	$6$	154.a	1.a	$1$	$5$	$5$	$24.699$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(20\)	\(25\)	\(25\)	\(245\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+4q^{2}+(5-\beta _{1})q^{3}+2^{4}q^{4}+(5-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(154)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)