Space of modular forms of level 1274, weight 2, and Character 1274.g

• Label: 1274.2.g
• Level: $1274$
• Weight: $2$
• Character orbit: 1274.g
• Rep. character: $\chi_{1274}(295,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $98$
• Newform subspaces: $19$
• Sturm bound: $392$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(392\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1274, [\chi])\).

	Total	New	Old
Modular forms	424	98	326
Cusp forms	360	98	262
Eisenstein series	64	0	64

Trace form

98 * q - q^2 - 49 * q^4 - 2 * q^5 + 2 * q^8 - 57 * q^9 + 5 * q^10 + 8 * q^11 - q^13 + 8 * q^15 - 49 * q^16 + 9 * q^17 + 26 * q^18 - 16 * q^19 + q^20 + 4 * q^23 + 88 * q^25 - 5 * q^26 - 24 * q^27 + 5 * q^29 + 4 * q^30 - 16 * q^31 - q^32 + 32 * q^33 + 6 * q^34 - 57 * q^36 + 37 * q^37 - 32 * q^38 - 16 * q^39 - 10 * q^40 + 5 * q^41 + 24 * q^43 - 16 * q^44 - 23 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^50 - 56 * q^51 + 2 * q^52 - 10 * q^53 - 12 * q^54 + 8 * q^55 - 24 * q^57 + 29 * q^58 + 12 * q^59 - 16 * q^60 + 25 * q^61 + 16 * q^62 + 98 * q^64 + 57 * q^65 + 16 * q^66 - 52 * q^67 + 9 * q^68 - 4 * q^69 + 4 * q^71 - 13 * q^72 + 14 * q^73 - 7 * q^74 + 40 * q^75 - 16 * q^76 - 8 * q^78 + 96 * q^79 + q^80 - 105 * q^81 + q^82 + 24 * q^83 - 29 * q^85 + 8 * q^86 - 20 * q^87 - 34 * q^89 - 58 * q^90 - 8 * q^92 - 24 * q^93 - 8 * q^94 - 8 * q^95 - 10 * q^97 - 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1274, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1274.2.g.a	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					26.2.c.a	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}+\cdots\)
1274.2.g.b	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.g.d	$2$	$0$	\(1\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.c	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.g.c	$2$	$0$	\(1\)	\(-2\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.d	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.e.b	$2$	$0$	\(1\)	\(-1\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.e	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.e.a	$2$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.f	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None		✓			1274.2.g.f	$2$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.g	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.g.b	$2$	$0$	\(1\)	\(1\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.h	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.e.a	$2$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.i	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None		✓			1274.2.g.f	$2$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.j	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.e.b	$2$	$0$	\(1\)	\(1\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.k	$1274$	$2$	1274.g	13.c	$3$	$2$	$1$	$10.173$	\(\Q(\sqrt{-3}) \)	None					182.2.g.a	$2$	$0$	\(1\)	\(3\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1274.2.g.l	$1274$	$2$	1274.g	13.c	$3$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					182.2.g.e	$2$	$0$	\(-2\)	\(0\)	\(-8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_1 q^{2}-\beta_{2} q^{3}+(\beta_1-1)q^{4}+\cdots\)
1274.2.g.m	$1274$	$2$	1274.g	13.c	$3$	$6$	$3$	$10.173$	6.0.4740147.1	None					182.2.e.c	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
1274.2.g.n	$1274$	$2$	1274.g	13.c	$3$	$6$	$3$	$10.173$	6.0.4740147.1	None					182.2.e.c	$2$	$0$	\(3\)	\(1\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}-\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1274.2.g.o	$1274$	$2$	1274.g	13.c	$3$	$8$	$4$	$10.173$	8.0.\(\cdots\).2	None		✓			1274.2.g.o	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
1274.2.g.p	$1274$	$2$	1274.g	13.c	$3$	$10$	$5$	$10.173$	10.0.\(\cdots\).1	None					182.2.e.d	$2$	$0$	\(-5\)	\(-1\)	\(4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+\beta _{6}q^{3}+\beta _{3}q^{4}-\beta _{8}q^{5}+\cdots\)
1274.2.g.q	$1274$	$2$	1274.g	13.c	$3$	$10$	$5$	$10.173$	10.0.\(\cdots\).1	None					182.2.e.d	$2$	$0$	\(-5\)	\(1\)	\(-4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}-\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{8}q^{5}+\cdots\)
1274.2.g.r	$1274$	$2$	1274.g	13.c	$3$	$16$	$8$	$10.173$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1274.2.g.r	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{8}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1274.2.g.s	$1274$	$2$	1274.g	13.c	$3$	$16$	$8$	$10.173$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1274.2.g.s	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{11})q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1274, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1274, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)