Space of modular forms of level 275, weight 4, and Character 275.b

• Label: 275.4.b
• Level: $275$
• Weight: $4$
• Character orbit: 275.b
• Rep. character: $\chi_{275}(199,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $7$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(275, [\chi])\).

	Total	New	Old
Modular forms	96	44	52
Cusp forms	84	44	40
Eisenstein series	12	0	12

Trace form

\( 44 q - 192 q^{4} - 8 q^{6} - 336 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(275, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.4.b.a	$275$	$4$	275.b	5.b	$2$	$2$	$2$	$16.226$	\(\Q(\sqrt{-1}) \)	None					55.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}+7q^{4}-3q^{6}-9iq^{7}+\cdots\)
275.4.b.b	$275$	$4$	275.b	5.b	$2$	$4$	$4$	$16.226$	\(\Q(i, \sqrt{17})\)	None					55.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-5+\cdots)q^{4}+\cdots\)
275.4.b.c	$275$	$4$	275.b	5.b	$2$	$4$	$4$	$16.226$	\(\Q(\zeta_{12})\)	None					11.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-4\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
275.4.b.d	$275$	$4$	275.b	5.b	$2$	$6$	$6$	$16.226$	6.0.5161984.1	None					55.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}+\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
275.4.b.e	$275$	$4$	275.b	5.b	$2$	$8$	$8$	$16.226$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					55.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-5+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.b.f	$275$	$4$	275.b	5.b	$2$	$10$	$10$	$16.226$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			275.4.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{8})q^{3}+(-8+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.b.g	$275$	$4$	275.b	5.b	$2$	$10$	$10$	$16.226$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			275.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

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