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

• Label: 275.2.l
• Level: $275$
• Weight: $2$
• Character orbit: 275.l
• Rep. character: $\chi_{275}(31,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $112$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.l (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(60\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

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

Trace form

112 * q - 6 * q^2 - 4 * q^3 + 98 * q^4 + q^6 - 9 * q^7 - 18 * q^8 - 28 * q^9 - 12 * q^10 - q^11 - 42 * q^12 - 13 * q^13 - 3 * q^14 + 16 * q^15 + 46 * q^16 - 2 * q^17 - 21 * q^18 - 30 * q^19 + q^20 - q^21 + q^22 + 12 * q^23 - 18 * q^24 - 14 * q^25 - 23 * q^26 + 5 * q^27 - 47 * q^28 - 54 * q^29 + 35 * q^30 + 3 * q^31 - 82 * q^32 + 16 * q^33 - 8 * q^34 + 18 * q^35 - 25 * q^36 - 2 * q^37 + 34 * q^38 + 47 * q^39 - 16 * q^40 + 27 * q^41 + 23 * q^42 + 44 * q^43 + q^44 - 20 * q^45 - 9 * q^46 - 6 * q^47 - 94 * q^48 - 33 * q^49 - 36 * q^50 + 7 * q^51 - 39 * q^52 + q^53 - 17 * q^54 + 27 * q^55 - 19 * q^56 - 60 * q^57 + 66 * q^58 + 13 * q^59 + 46 * q^60 + 6 * q^61 + 52 * q^62 - 4 * q^63 - 10 * q^64 - 24 * q^65 - 12 * q^66 - 35 * q^67 + q^68 + 44 * q^69 - 33 * q^70 + 21 * q^71 - 54 * q^72 + 40 * q^73 + q^74 - 44 * q^75 - 130 * q^76 + 86 * q^77 + 11 * q^78 + 11 * q^79 - 124 * q^80 - 18 * q^81 - 50 * q^82 - 93 * q^83 - 14 * q^84 - 6 * q^85 + 26 * q^86 + 48 * q^87 + 31 * q^88 + 24 * q^89 + 109 * q^90 + 40 * q^91 - 68 * q^92 - 43 * q^93 + 25 * q^94 - 16 * q^95 + 40 * q^96 - 44 * q^97 + 112 * q^98 - 63 * 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.l.a	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	\(\Q(\zeta_{10})\)	None		✓			275.2.k.c	$2$	$1$	\(-4\)	\(-5\)	\(-5\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-q^{2}+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
275.2.l.b	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	\(\Q(\zeta_{10})\)	None		✓			275.2.k.b	$2$	$1$	\(-2\)	\(-1\)	\(-5\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots\)
275.2.l.c	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	\(\Q(\zeta_{10})\)	None		✓			275.2.k.a	$2$	$0$	\(-2\)	\(4\)	\(5\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(2-\zeta_{10}+\cdots)q^{3}+\cdots\)
275.2.l.d	$275$	$2$	275.l	275.l	$5$	$100$	$25$	$2.196$		None		✓	✓		275.2.k.d	$2$	$0$	\(2\)	\(-2\)	\(5\)	\(5\)		$\mathrm{SU}(2)[C_{5}]$