Space of modular forms of level 1421, weight 2, and Character 1421.b

• Label: 1421.2.b
• Level: $1421$
• Weight: $2$
• Character orbit: 1421.b
• Rep. character: $\chi_{1421}(1275,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $12$
• Sturm bound: $280$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1421.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(280\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1421, [\chi])\).

	Total	New	Old
Modular forms	148	108	40
Cusp forms	132	98	34
Eisenstein series	16	10	6

Trace form

98 * q - 90 * q^4 + 2 * q^5 + 2 * q^6 - 88 * q^9 + 6 * q^13 + 90 * q^16 + 18 * q^20 - 6 * q^22 - 12 * q^23 + 14 * q^24 + 76 * q^25 + 2 * q^29 + 34 * q^30 - 26 * q^33 - 4 * q^34 + 48 * q^36 + 20 * q^38 - 24 * q^45 + 28 * q^51 - 18 * q^52 - 6 * q^53 - 34 * q^54 - 20 * q^57 - 32 * q^58 + 12 * q^59 + 10 * q^62 - 146 * q^64 + 18 * q^65 - 12 * q^67 - 64 * q^71 + 44 * q^74 - 10 * q^78 - 2 * q^80 + 138 * q^81 - 28 * q^82 - 44 * q^83 - 74 * q^86 - 4 * q^87 - 66 * q^88 + 144 * q^92 + 30 * q^93 + 14 * q^94 + 50 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(1421, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1421.2.b.a	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		✓			1421.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-5q^{4}+3\beta q^{8}+3q^{9}-2\beta q^{11}+\cdots\)
1421.2.b.b	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	\(\Q(\sqrt{-5}) \)	None					29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+\beta q^{3}-3q^{4}+3q^{5}-5q^{6}+\cdots\)
1421.2.b.c	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	\(\Q(\sqrt{-5}) \)	None					203.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+2q^{4}-2q^{5}-2q^{9}-2\beta q^{11}+\cdots\)
1421.2.b.d	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.7168.1	None		✓			1421.2.b.d	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1421.2.b.e	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.7168.1	None		✓			1421.2.b.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1421.2.b.f	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.94192.1	\(\Q(\sqrt{-203}) \)		✓			1421.2.b.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+2q^{4}+(-3+\beta _{2})q^{9}+2\beta _{1}q^{12}+\cdots\)
1421.2.b.g	$1421$	$2$	1421.b	29.b	$2$	$6$	$6$	$11.347$	6.0.16516096.1	None					203.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1421.2.b.h	$1421$	$2$	1421.b	29.b	$2$	$6$	$6$	$11.347$	6.0.25809920.1	None					203.2.b.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1421.2.b.i	$1421$	$2$	1421.b	29.b	$2$	$12$	$12$	$11.347$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1421.2.b.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}-\beta _{8}q^{3}+(-1-\beta _{5})q^{4}-\beta _{2}q^{5}+\cdots\)
1421.2.b.j	$1421$	$2$	1421.b	29.b	$2$	$18$	$18$	$11.347$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					203.2.j.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1421.2.b.k	$1421$	$2$	1421.b	29.b	$2$	$18$	$18$	$11.347$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					203.2.j.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1421.2.b.l	$1421$	$2$	1421.b	29.b	$2$	$20$	$20$	$11.347$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		1421.2.b.l	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{16}q^{2}+\beta _{13}q^{3}+(-1-\beta _{8})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1421, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1421, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 2}\)