Space of modular forms of level 242, weight 2, and Character 242.c

• Label: 242.2.c
• Level: $242$
• Weight: $2$
• Character orbit: 242.c
• Rep. character: $\chi_{242}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $66$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(66\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(242, [\chi])\).

	Total	New	Old
Modular forms	180	36	144
Cusp forms	84	36	48
Eisenstein series	96	0	96

Trace form

36 * q + q^2 + 6 * q^3 - 9 * q^4 + 8 * q^5 - q^6 - 2 * q^7 + q^8 - 15 * q^9 - 4 * q^10 - 14 * q^12 + 4 * q^13 - 2 * q^14 - 2 * q^15 - 9 * q^16 - 2 * q^17 + 8 * q^18 + 5 * q^19 + 8 * q^20 + 12 * q^21 - 12 * q^23 - q^24 - 13 * q^25 - 4 * q^26 + 3 * q^27 - 2 * q^28 - 10 * q^29 - 6 * q^30 + 10 * q^31 - 4 * q^32 - 18 * q^34 - 12 * q^35 + 28 * q^37 - 8 * q^38 + 6 * q^39 - 4 * q^40 + 2 * q^41 + 6 * q^42 - 6 * q^43 - 12 * q^45 + 4 * q^46 + 16 * q^47 + 6 * q^48 - 5 * q^49 + 11 * q^50 + 7 * q^51 - 6 * q^52 + 10 * q^53 + 8 * q^56 - 5 * q^57 - 4 * q^58 + q^59 + 8 * q^60 - 8 * q^61 + 2 * q^62 - 16 * q^63 - 9 * q^64 - 16 * q^65 - 94 * q^67 - 2 * q^68 + 2 * q^69 + 16 * q^70 + 4 * q^71 - 7 * q^72 + 14 * q^73 + 18 * q^74 + 31 * q^75 + 10 * q^76 - 16 * q^78 + 30 * q^79 - 2 * q^80 + 19 * q^82 + 19 * q^83 - 8 * q^84 - 2 * q^85 - 11 * q^86 + 20 * q^87 - 54 * q^89 - 12 * q^90 - 52 * q^91 - 2 * q^92 - 62 * q^93 - 12 * q^94 + 10 * q^95 + 4 * q^96 - 57 * q^97 + 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(242, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
242.2.c.a	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(-1\)	\(1\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
242.2.c.b	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	\(\Q(\zeta_{10})\)	None		✓			242.2.a.a	$4$	$0$	\(-1\)	\(2\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
242.2.c.c	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(1\)	\(-4\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
242.2.c.d	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(1\)	\(1\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
242.2.c.e	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	\(\Q(\zeta_{10})\)	None		✓			242.2.a.a	$4$	$0$	\(1\)	\(2\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-2\zeta_{10}^{2}q^{3}+\cdots\)
242.2.c.f	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		✓			242.2.a.c	$4$	$0$	\(-2\)	\(2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
242.2.c.g	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		✓			242.2.a.c	$4$	$0$	\(2\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(242, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(242, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)