Space of modular forms of level 154, weight 4, and trivial character

• Label: 154.4.a
• Level: $154$
• Weight: $4$
• Character orbit: 154.a
• Rep. character: $\chi_{154}(1,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $9$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	154.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(154))\).

	Total	New	Old
Modular forms	76	14	62
Cusp forms	68	14	54
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
\(+\)	\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
Plus space			\(+\)	\(9\)
Minus space			\(-\)	\(5\)

Trace form

\( 14 q + 4 q^{2} - 8 q^{3} + 56 q^{4} + 36 q^{5} + 16 q^{8} + 154 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(154))\) 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	7	11
154.4.a.a	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	\(\Q\)	None	✓	✓	✓	✓	154.4.a.a	$1$	$0$	\(-2\)	\(-5\)	\(-1\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-5q^{3}+4q^{4}-q^{5}+10q^{6}+\cdots\)
154.4.a.b	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	\(\Q\)	None	✓	✓	✓	✓	154.4.a.b	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+2q^{5}-7q^{7}-8q^{8}+\cdots\)
154.4.a.c	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	\(\Q\)	None	✓	✓			154.4.a.c	$1$	$0$	\(2\)	\(-10\)	\(-14\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-10q^{3}+4q^{4}-14q^{5}-20q^{6}+\cdots\)
154.4.a.d	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	\(\Q\)	None	✓	✓			154.4.a.d	$1$	$0$	\(2\)	\(-2\)	\(18\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots\)
154.4.a.e	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	\(\Q\)	None	✓	✓			154.4.a.e	$1$	$0$	\(2\)	\(7\)	\(3\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+7q^{3}+4q^{4}+3q^{5}+14q^{6}+\cdots\)
154.4.a.f	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	\(\Q(\sqrt{137}) \)	None	✓	✓	✓	✓	154.4.a.f	$1$	$1$	\(-4\)	\(-5\)	\(-7\)	\(14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
154.4.a.g	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	\(\Q(\sqrt{37}) \)	None	✓	✓	✓	✓	154.4.a.g	$1$	$0$	\(-4\)	\(6\)	\(26\)	\(14\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots\)
154.4.a.h	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	\(\Q(\sqrt{57}) \)	None	✓	✓	✓	✓	154.4.a.h	$1$	$1$	\(4\)	\(-5\)	\(-17\)	\(-14\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots\)
154.4.a.i	$154$	$4$	154.a	1.a	$1$	$3$	$3$	$9.086$	3.3.7636.1	None	✓	✓	✓	✓	154.4.a.i	$1$	$0$	\(6\)	\(6\)	\(26\)	\(-21\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

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