Space of modular forms of level 275, weight 3, and Character 275.q

• Label: 275.3.q
• Level: $275$
• Weight: $3$
• Character orbit: 275.q
• Rep. character: $\chi_{275}(24,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $136$
• Newform subspaces: $7$
• Sturm bound: $90$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(90\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(275, [\chi])\).

	Total	New	Old
Modular forms	264	152	112
Cusp forms	216	136	80
Eisenstein series	48	16	32

Trace form

136 * q - 58 * q^4 - 10 * q^6 + 118 * q^9 - 2 * q^11 - 34 * q^14 + 10 * q^16 + 10 * q^19 + 50 * q^24 - 196 * q^26 + 10 * q^29 - 124 * q^31 + 256 * q^34 - 188 * q^36 + 330 * q^39 - 130 * q^41 - 286 * q^44 - 460 * q^46 - 258 * q^49 + 510 * q^51 + 488 * q^56 - 158 * q^59 + 420 * q^61 + 418 * q^64 + 1540 * q^66 - 286 * q^69 - 588 * q^71 - 1250 * q^74 - 550 * q^79 - 780 * q^81 + 1460 * q^84 - 486 * q^86 + 228 * q^89 - 876 * q^91 - 640 * q^94 - 2700 * q^96 - 1054 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(275, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.3.q.a	$275$	$3$	275.q	55.h	$10$	$8$	$2$	$7.493$	\(\Q(\zeta_{20})\)	None					55.3.i.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{20}+\zeta_{20}^{3}+\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots\)
275.3.q.b	$275$	$3$	275.q	55.h	$10$	$8$	$2$	$7.493$	\(\Q(\zeta_{20})\)	None		✓			275.3.x.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta_{6}-\beta_{5})q^{2}+(-2\beta_{7}+2\beta_{6}-2\beta_{5})q^{3}+\cdots\)
275.3.q.c	$275$	$3$	275.q	55.h	$10$	$8$	$2$	$7.493$	\(\Q(\zeta_{20})\)	None					55.3.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-2\zeta_{20}-2\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+4\zeta_{20}q^{3}+\cdots\)
275.3.q.d	$275$	$3$	275.q	55.h	$10$	$8$	$2$	$7.493$	\(\Q(\zeta_{20})\)	None					11.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta_{7}+\beta_{6}-\beta_{2})q^{2}+(-\beta_{7}-\beta_{2})q^{3}+\cdots\)
275.3.q.e	$275$	$3$	275.q	55.h	$10$	$24$	$6$	$7.493$		None					55.3.i.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
275.3.q.f	$275$	$3$	275.q	55.h	$10$	$24$	$6$	$7.493$		None					55.3.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
275.3.q.g	$275$	$3$	275.q	55.h	$10$	$56$	$14$	$7.493$		None		✓	✓		275.3.x.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(275, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)