Space of modular forms of level 275, weight 2, and Character 275.i

• Label: 275.2.i
• Level: $275$
• Weight: $2$
• Character orbit: 275.i
• Rep. character: $\chi_{275}(56,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $104$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.i (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

	Total	New	Old
Modular forms	128	104	24
Cusp forms	112	104	8
Eisenstein series	16	0	16

Trace form

\( 104 q - 2 q^{2} - 2 q^{3} - 28 q^{4} + 12 q^{8} - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.i.a	$275$	$2$	275.i	25.d	$5$	$44$	$11$	$2.196$		None		$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$
275.2.i.b	$275$	$2$	275.i	25.d	$5$	$60$	$15$	$2.196$		None		$2$	$0$	\(-1\)	\(-2\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

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