Newform orbit 275.3.o.a

• Label: 275.3.o.a
• Level: $275$
• Weight: $3$
• Character orbit: 275.o
• Analytic conductor: $7.493$
• Analytic rank: $0$
• Dimension: $232$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.49320726991\)
Analytic rank:	\(0\)
Dimension:	\(232\)
Relative dimension:	\(58\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 232 * q - 5 * q^2 - 113 * q^4 - 3 * q^5 + 15 * q^6 - 35 * q^7 - 5 * q^8 - 664 * q^9 + 60 * q^10 + 12 * q^11 - 50 * q^12 - 10 * q^13 + 15 * q^14 - 6 * q^15 - 213 * q^16 - 40 * q^17 + 45 * q^18 + 45 * q^19 + 27 * q^20 + 45 * q^21 + 60 * q^22 - 10 * q^23 - 110 * q^24 - 93 * q^25 - 5 * q^26 + 235 * q^28 - 5 * q^29 + 40 * q^30 - 26 * q^31 + 550 * q^32 - 115 * q^33 - 10 * q^34 + 155 * q^35 + 216 * q^36 + 200 * q^37 - 185 * q^38 - 5 * q^40 + 70 * q^41 + 65 * q^42 + 27 * q^44 + 66 * q^45 - 5 * q^46 + 40 * q^48 - 243 * q^49 + 240 * q^50 + 35 * q^51 + 175 * q^52 + 10 * q^53 + 205 * q^54 - 208 * q^55 - 75 * q^56 - 240 * q^57 - 320 * q^58 + 29 * q^59 - 431 * q^60 + 380 * q^62 + 215 * q^63 - 193 * q^64 + 130 * q^65 + 375 * q^66 + 645 * q^67 + 325 * q^68 - 312 * q^69 - 515 * q^70 + 84 * q^71 - 280 * q^72 - 140 * q^73 - 305 * q^74 - 86 * q^75 + 430 * q^77 - 345 * q^78 - 405 * q^79 + 167 * q^80 + 1560 * q^81 - 70 * q^82 + 295 * q^83 + 510 * q^84 - 60 * q^85 + 155 * q^86 - 440 * q^88 - 216 * q^89 - 1165 * q^90 + 10 * q^91 + 85 * q^93 - 510 * q^94 + 230 * q^95 - 5 * q^97 + 180 * q^98 - 769 * q^99

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
79.1	−3.14190	−	2.28273i		−	5.06285i	3.42465	+	10.5400i	−3.67310	−	3.39240i	−11.5571	+	15.9070i	−5.95490	−	4.32649i	8.49960	−	26.1591i	−16.6325			3.79661	+	19.0433i
79.2	−3.07776	−	2.23612i		−	1.87514i	3.23629	+	9.96029i	1.20593	+	4.85239i	−4.19304	+	5.77123i	0.347121	+	0.252198i	7.60951	−	23.4197i	5.48386			7.13899	−	17.6311i
79.3	−3.00943	−	2.18648i			5.62007i	3.03991	+	9.35589i	−4.78783	+	1.44107i	12.2882	−	16.9132i	−6.70263	−	4.86975i	6.71006	−	20.6514i	−22.5852			17.5595	+	6.13170i
79.4	−2.99003	−	2.17238i			3.39489i	2.98495	+	9.18674i	4.83959	+	1.25632i	7.37500	−	10.1508i	4.40043	+	3.19710i	6.46366	−	19.8931i	−2.52527			−11.7413	−	14.2699i
79.5	−2.89672	−	2.10459i			2.31904i	2.72563	+	8.38861i	−1.70902	−	4.69886i	4.88064	−	6.71762i	7.63209	+	5.54504i	5.33343	−	16.4146i	3.62205			−4.93863	+	17.2081i
79.6	−2.74593	−	1.99503i		−	2.57957i	2.32389	+	7.15221i	4.69147	−	1.72919i	−5.14634	+	7.08332i	0.360984	+	0.262271i	3.69225	−	11.3636i	2.34580			−16.3322	−	4.61142i
79.7	−2.63158	−	1.91195i			1.64408i	2.03357	+	6.25869i	0.245385	−	4.99398i	3.14341	−	4.32653i	−8.36489	−	6.07745i	2.59412	−	7.98389i	6.29700			−10.1940	+	12.6729i
79.8	−2.45899	−	1.78656i		−	1.79742i	1.61877	+	4.98208i	−4.72288	−	1.64146i	−3.21121	+	4.41985i	4.25966	+	3.09482i	1.16323	−	3.58006i	5.76928			8.68096	+	12.4741i
79.9	−2.40209	−	1.74522i		−	4.78503i	1.48817	+	4.58012i	0.0307584	+	4.99991i	−8.35094	+	11.4941i	7.94422	+	5.77181i	0.748532	−	2.30374i	−13.8966			8.65205	−	12.0639i
79.10	−2.34572	−	1.70426i			1.09216i	1.36181	+	4.19123i	1.67422	+	4.71137i	1.86134	−	2.56191i	−11.0864	−	8.05477i	0.364591	−	1.12210i	7.80718			4.10218	−	13.9049i
79.11	−2.28174	−	1.65778i		−	2.89615i	1.22204	+	3.76105i	4.32248	−	2.51320i	−4.80120	+	6.60828i	−1.65501	−	1.20243i	−0.0395671	+	0.121775i	0.612293			−14.0291	−	1.43124i
79.12	−2.27836	−	1.65533i			0.726019i	1.21475	+	3.73863i	−4.48388	+	2.21242i	1.20180	−	1.65413i	1.30618	+	0.948997i	−0.0600228	+	0.184731i	8.47290			13.8782	+	2.38161i
79.13	−2.09811	−	1.52437i			3.94223i	0.842313	+	2.59237i	−1.92213	+	4.61578i	6.00941	−	8.27124i	7.52224	+	5.46523i	−1.02117	+	3.14283i	−6.54115			11.0690	−	6.75438i
79.14	−1.84159	−	1.33799i		−	4.05298i	0.365158	+	1.12384i	−3.74199	+	3.31625i	−5.42286	+	7.46393i	−10.6263	−	7.72045i	−1.98248	+	6.10144i	−7.42668			11.3283	−	1.10042i
79.15	−1.83881	−	1.33597i			5.56642i	0.360329	+	1.10898i	3.37354	−	3.69042i	7.43659	−	10.2356i	−0.872374	−	0.633817i	−1.99046	+	6.12602i	−21.9850			−11.1336	+	2.27902i
79.16	−1.82824	−	1.32829i			3.42073i	0.342024	+	1.05264i	2.82819	+	4.12327i	4.54372	−	6.25390i	−0.171387	−	0.124520i	−2.02038	+	6.21810i	−2.70137			0.306296	−	11.2950i
79.17	−1.68131	−	1.22154i		−	5.71087i	0.0985661	+	0.303355i	0.203030	−	4.99588i	−6.97607	+	9.60173i	6.53064	+	4.74479i	−2.36397	+	7.27555i	−23.6140			−6.44403	+	8.15160i
79.18	−1.45733	−	1.05881i			1.75333i	−0.233343	−	0.718155i	4.13050	−	2.81762i	1.85644	−	2.55517i	3.89661	+	2.83105i	−2.64693	+	8.14642i	5.92584			−9.00282	−	0.267215i
79.19	−1.27452	−	0.925995i			4.14372i	−0.469127	−	1.44382i	−4.73555	−	1.60455i	3.83707	−	5.28127i	−2.97342	−	2.16032i	−2.68636	+	8.26776i	−8.17044			4.54976	+	6.43013i
79.20	−1.25828	−	0.914191i		−	1.39013i	−0.488554	−	1.50362i	4.38926	+	2.39465i	−1.27085	+	1.74917i	−0.382152	−	0.277650i	−2.68233	+	8.25537i	7.06753			−3.33373	−	7.02576i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
275.o	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	275.3.o.a	✓	232
11.d	odd	10	1		275.3.bd.a	yes	232
25.e	even	10	1		275.3.bd.a	yes	232
275.o	odd	10	1	inner	275.3.o.a	✓	232

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
275.3.o.a	✓	232	1.a	even	1	1	trivial
275.3.o.a	✓	232	275.o	odd	10	1	inner
275.3.bd.a	yes	232	11.d	odd	10	1
275.3.bd.a	yes	232	25.e	even	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(275, [\chi])\).