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 - 12 * q^10 - 4 * q^11 + 12 * q^12 - 16 * q^13 - 20 * q^14 + 21 * q^15 - 32 * q^16 - 28 * q^17 - 4 * q^18 + 16 * q^20 - 12 * q^21 - 6 * q^23 - 28 * q^24 - 4 * q^25 + 36 * q^26 - 5 * q^27 - 44 * q^28 - 4 * q^29 + 10 * q^30 - 18 * q^31 - 8 * q^32 - 2 * q^33 - 10 * q^34 - 42 * q^35 + 12 * q^36 + 42 * q^37 + 44 * q^38 + 24 * q^39 - 66 * q^40 - 24 * q^41 - 4 * q^42 + 56 * q^43 - 10 * q^44 - 50 * q^45 - 40 * q^46 - 2 * q^47 + 48 * q^48 + 136 * q^49 - 6 * q^50 - 44 * q^51 + 70 * q^52 + 28 * q^53 + 78 * q^54 - 3 * q^55 - 24 * q^56 - 80 * q^57 - 24 * q^58 + 3 * q^59 + 36 * q^60 - 40 * q^61 - 52 * q^63 - 46 * q^64 + 46 * q^65 - 8 * q^66 + 29 * q^67 + 104 * q^68 + 21 * q^69 - 88 * q^70 - 20 * q^71 + 56 * q^72 + 32 * q^73 - 56 * q^74 - 39 * q^75 - 60 * q^76 - 70 * q^78 + 16 * q^79 + 186 * q^80 + 29 * q^81 - 92 * q^82 + 44 * q^83 + 44 * q^84 + 34 * q^85 - 30 * q^86 - 2 * q^87 + 36 * q^88 + 14 * q^89 + 144 * q^90 + 4 * q^91 + 136 * q^92 - 104 * q^93 - 52 * q^94 + 4 * q^95 + 124 * q^96 - 60 * q^97 - 170 * q^98 + 38 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.i.a	$275$	$2$	275.i	25.d	$5$	$44$	$11$	$2.196$		None		✓			275.2.i.a	$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$
275.2.i.b	$275$	$2$	275.i	25.d	$5$	$60$	$15$	$2.196$		None		✓	✓		275.2.i.b	$2$	$0$	\(-1\)	\(-2\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

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

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