Space of modular forms of level 121, weight 4, and Character 121.c

• Label: 121.4.c
• Level: $121$
• Weight: $4$
• Character orbit: 121.c
• Rep. character: $\chi_{121}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $92$
• Newform subspaces: $10$
• Sturm bound: $44$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(44\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(121, [\chi])\).

	Total	New	Old
Modular forms	156	124	32
Cusp forms	108	92	16
Eisenstein series	48	32	16

Trace form

\( 92 q + 7 q^{2} + 5 q^{3} - 83 q^{4} + 3 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} - 182 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
121.4.c.a	$121$	$4$	121.c	11.c	$5$	$4$	$1$	$7.139$	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-11}) \)		$8$	$0$	\(0\)	\(-8\)	\(-18\)	\(0\)	$1$	$\mathrm{U}(1)[D_{5}]$	\(q+8\zeta_{10}^{2}q^{3}+8\zeta_{10}^{3}q^{4}-18\zeta_{10}q^{5}+\cdots\)
121.4.c.b	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None		$2$	$0$	\(-3\)	\(-3\)	\(18\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
121.4.c.c	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		$4$	$0$	\(-2\)	\(2\)	\(-2\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}+\beta _{7})q^{2}+(-4\beta _{1}-\beta _{6})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.d	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		$4$	$0$	\(-2\)	\(8\)	\(10\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}-\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.e	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(10\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}-5\beta _{6}q^{3}+18\beta _{4}q^{4}+(-5+\cdots)q^{5}+\cdots\)
121.4.c.f	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		$4$	$0$	\(2\)	\(2\)	\(-2\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+(4\beta _{1}-\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.g	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		$4$	$0$	\(2\)	\(8\)	\(10\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.h	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None		$2$	$0$	\(3\)	\(-3\)	\(18\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+2\beta _{4}+\beta _{6}-\beta _{7})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.i	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None		$2$	$0$	\(7\)	\(-3\)	\(-7\)	\(35\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.j	$121$	$4$	121.c	11.c	$5$	$24$	$6$	$7.139$		None		$8$	$0$	\(0\)	\(-8\)	\(-14\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(121, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(121, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)