Space of modular forms of level 275, weight 6, and Character 275.b

• Label: 275.6.b
• Level: $275$
• Weight: $6$
• Character orbit: 275.b
• Rep. character: $\chi_{275}(199,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $8$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(275, [\chi])\).

	Total	New	Old
Modular forms	156	76	80
Cusp forms	144	76	68
Eisenstein series	12	0	12

Trace form

76 * q - 1208 * q^4 + 520 * q^6 - 7302 * q^9 + 484 * q^11 + 2260 * q^14 + 18032 * q^16 - 5940 * q^19 - 15248 * q^21 + 8012 * q^24 + 23624 * q^26 - 22064 * q^29 + 14998 * q^31 + 75040 * q^34 + 112968 * q^36 + 30924 * q^39 - 62176 * q^41 - 14520 * q^44 - 53280 * q^46 - 214944 * q^49 - 57716 * q^51 - 52412 * q^54 - 86916 * q^56 - 98762 * q^59 - 170820 * q^61 - 554116 * q^64 + 34848 * q^66 + 57146 * q^69 + 313850 * q^71 + 148044 * q^74 + 96420 * q^76 + 23936 * q^79 + 183676 * q^81 + 1133644 * q^84 - 382700 * q^86 + 93614 * q^89 + 78476 * q^91 - 105992 * q^94 - 19584 * q^96 - 2662 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(275, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.6.b.a	$275$	$6$	275.b	5.b	$2$	$2$	$2$	$44.106$	\(\Q(\sqrt{-1}) \)	None					11.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{2}-15 i q^{3}+16 q^{4}+60 q^{6}+\cdots\)
275.6.b.b	$275$	$6$	275.b	5.b	$2$	$6$	$6$	$44.106$	6.0.\(\cdots\).1	None					11.6.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(6\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-30+\cdots)q^{4}+\cdots\)
275.6.b.c	$275$	$6$	275.b	5.b	$2$	$6$	$6$	$44.106$	6.0.\(\cdots\).1	None					55.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+(-14+\cdots)q^{4}+\cdots\)
275.6.b.d	$275$	$6$	275.b	5.b	$2$	$8$	$8$	$44.106$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					55.6.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-15+\beta _{3}+\cdots)q^{4}+\cdots\)
275.6.b.e	$275$	$6$	275.b	5.b	$2$	$10$	$10$	$44.106$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					55.6.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-23+\beta _{1}+\cdots)q^{4}+\cdots\)
275.6.b.f	$275$	$6$	275.b	5.b	$2$	$12$	$12$	$44.106$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					55.6.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(-19+\beta _{2}+\cdots)q^{4}+\cdots\)
275.6.b.g	$275$	$6$	275.b	5.b	$2$	$16$	$16$	$44.106$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			275.6.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(-14+\beta _{2}+\cdots)q^{4}+\cdots\)
275.6.b.h	$275$	$6$	275.b	5.b	$2$	$16$	$16$	$44.106$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			275.6.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+(\beta _{9}-\beta _{11})q^{3}+(-11+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(275, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)