Space of modular forms of level 704, weight 2, and Character 704.m

• Label: 704.2.m
• Level: $704$
• Weight: $2$
• Character orbit: 704.m
• Rep. character: $\chi_{704}(257,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $88$
• Newform subspaces: $14$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.m (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(704, [\chi])\).

	Total	New	Old
Modular forms	432	104	328
Cusp forms	336	88	248
Eisenstein series	96	16	80

Trace form

88 * q + 6 * q^5 - 24 * q^9 + 6 * q^13 - 6 * q^17 + 4 * q^21 - 20 * q^25 - 10 * q^29 - 10 * q^33 + 30 * q^37 - 22 * q^41 - 112 * q^45 - 16 * q^49 + 54 * q^53 - 10 * q^57 + 6 * q^61 + 4 * q^65 + 48 * q^69 - 6 * q^73 + 10 * q^77 - 16 * q^81 + 34 * q^85 - 16 * q^89 + 18 * q^93 - 38 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(704, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.2.m.a	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(0\)	\(-4\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
704.2.m.b	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					88.2.i.a	$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
704.2.m.c	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					352.2.m.a	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
704.2.m.d	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					44.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
704.2.m.e	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					44.2.e.a	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
704.2.m.f	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					352.2.m.a	$2$	$0$	\(0\)	\(2\)	\(6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}+\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2})q^{5}+\cdots\)
704.2.m.g	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					88.2.i.a	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
704.2.m.h	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(0\)	\(4\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
704.2.m.i	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.682515625.5	None					88.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
704.2.m.j	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.484000000.6	None					352.2.m.d	$4$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
704.2.m.k	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.484000000.9	None					352.2.m.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
704.2.m.l	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.682515625.5	None					88.2.i.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
704.2.m.m	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					352.2.m.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
704.2.m.n	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					352.2.m.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{5}-\beta _{8})q^{3}-\beta _{9}q^{5}+(1-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(704, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)