Newform orbit 33.5.g.a

• Label: 33.5.g.a
• Level: $33$
• Weight: $5$
• Character orbit: 33.g
• Analytic conductor: $3.411$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.g (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.41120878177\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 76 q^{4} + 36 q^{5} + 150 q^{7} + 480 q^{8} - 216 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−4.37135	+	6.01665i	−1.60570	+	4.94183i	−12.1471	−	37.3849i	−24.8968	+	18.0886i	−22.7142	−	31.2634i	40.6127	−	13.1959i	164.863	+	53.5673i	−21.8435	−	15.8702i		−	228.867i
7.2	−4.20830	+	5.79223i	1.60570	−	4.94183i	−10.8958	−	33.5339i	33.2604	−	24.1651i	21.8670	+	30.0973i	−32.2093	+	10.4654i	131.142	+	42.6108i	−21.8435	−	15.8702i			294.346i
7.3	−2.44632	+	3.36708i	1.60570	−	4.94183i	−0.408428	−	1.25701i	−26.0050	+	18.8937i	12.7115	+	17.4958i	−15.8191	+	5.13994i	−58.1002	−	18.8779i	−21.8435	−	15.8702i		−	133.781i
7.4	−1.95593	+	2.69210i	−1.60570	+	4.94183i	1.52251	+	4.68579i	6.63359	−	4.81958i	−10.1633	−	13.9886i	−71.1959	+	23.1329i	−66.2286	−	21.5190i	−21.8435	−	15.8702i			27.2851i
7.5	−0.0886329	+	0.121993i	1.60570	−	4.94183i	4.93725	+	15.1953i	11.7622	−	8.54577i	0.460550	+	0.633892i	66.7007	−	21.6724i	−4.58589	−	1.49005i	−21.8435	−	15.8702i			2.19234i
7.6	1.01888	−	1.40237i	−1.60570	+	4.94183i	4.01574	+	12.3592i	−32.0081	+	23.2552i	5.29428	+	7.28695i	27.3116	−	8.87408i	47.8012	+	15.5316i	−21.8435	−	15.8702i			68.5817i
7.7	1.95429	−	2.68985i	−1.60570	+	4.94183i	1.52822	+	4.70338i	35.4362	−	25.7459i	10.1548	+	13.9769i	8.04612	−	2.61434i	66.2318	+	21.5200i	−21.8435	−	15.8702i		−	145.633i
7.8	3.38915	−	4.66477i	1.60570	−	4.94183i	−5.32944	−	16.4023i	4.81744	−	3.50008i	−17.6106	−	24.2389i	−13.8978	+	4.51567i	−6.83522	−	2.22090i	−21.8435	−	15.8702i		−	34.3346i
13.1	−7.29601	−	2.37062i	4.20378	−	3.05422i	34.6676	+	25.1875i	2.18122	+	6.71310i	−37.9112	+	12.3181i	28.6722	−	39.4639i	−121.078	−	166.650i	8.34346	−	25.6785i		−	54.1497i
13.2	−4.49285	−	1.45982i	−4.20378	+	3.05422i	5.11038	+	3.71291i	5.35863	+	16.4922i	23.3455	−	7.58543i	48.2339	−	66.3883i	26.8877	+	37.0078i	8.34346	−	25.6785i		−	81.9194i
13.3	−0.173259	−	0.0562952i	4.20378	−	3.05422i	−12.9174	−	9.38506i	−6.40673	−	19.7179i	−0.900279	+	0.292519i	12.6762	−	17.4473i	3.42300	+	4.71136i	8.34346	−	25.6785i			3.77697i
13.4	0.619915	+	0.201423i	−4.20378	+	3.05422i	−12.6005	−	9.15483i	12.5302	+	38.5641i	−3.22117	+	1.04662i	−44.8315	+	61.7053i	−12.0973	−	16.6506i	8.34346	−	25.6785i			26.4303i
13.5	0.743344	+	0.241527i	−4.20378	+	3.05422i	−12.4500	−	9.04549i	−9.71709	−	29.9061i	−3.86253	+	1.25501i	16.8776	−	23.2301i	−14.4205	−	19.8482i	8.34346	−	25.6785i		−	24.5775i
13.6	4.40557	+	1.43146i	4.20378	−	3.05422i	4.41572	+	3.20821i	12.7557	+	39.2579i	22.8920	−	7.43807i	37.7759	−	51.9941i	−28.7033	−	39.5067i	8.34346	−	25.6785i			191.213i
13.7	6.41780	+	2.08527i	4.20378	−	3.05422i	23.8955	+	17.3611i	−9.80980	−	30.1915i	33.3478	−	10.8354i	−46.3989	+	63.8626i	53.6911	+	73.8995i	8.34346	−	25.6785i		−	214.219i
13.8	6.48369	+	2.10668i	−4.20378	+	3.05422i	24.6559	+	17.9136i	2.10789	+	6.48741i	−33.6903	+	10.9466i	12.4454	−	17.1296i	58.0090	+	79.8425i	8.34346	−	25.6785i			46.5030i
19.1	−4.37135	−	6.01665i	−1.60570	−	4.94183i	−12.1471	+	37.3849i	−24.8968	−	18.0886i	−22.7142	+	31.2634i	40.6127	+	13.1959i	164.863	−	53.5673i	−21.8435	+	15.8702i			228.867i
19.2	−4.20830	−	5.79223i	1.60570	+	4.94183i	−10.8958	+	33.5339i	33.2604	+	24.1651i	21.8670	−	30.0973i	−32.2093	−	10.4654i	131.142	−	42.6108i	−21.8435	+	15.8702i		−	294.346i
19.3	−2.44632	−	3.36708i	1.60570	+	4.94183i	−0.408428	+	1.25701i	−26.0050	−	18.8937i	12.7115	−	17.4958i	−15.8191	−	5.13994i	−58.1002	+	18.8779i	−21.8435	+	15.8702i			133.781i
19.4	−1.95593	−	2.69210i	−1.60570	−	4.94183i	1.52251	−	4.68579i	6.63359	+	4.81958i	−10.1633	+	13.9886i	−71.1959	−	23.1329i	−66.2286	+	21.5190i	−21.8435	+	15.8702i		−	27.2851i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	33.5.g.a	✓	32
3.b	odd	2	1		99.5.k.c		32
11.c	even	5	1		363.5.c.e		32
11.d	odd	10	1	inner	33.5.g.a	✓	32
11.d	odd	10	1		363.5.c.e		32
33.f	even	10	1		99.5.k.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
33.5.g.a	✓	32	1.a	even	1	1	trivial
33.5.g.a	✓	32	11.d	odd	10	1	inner
99.5.k.c		32	3.b	odd	2	1
99.5.k.c		32	33.f	even	10	1
363.5.c.e		32	11.c	even	5	1
363.5.c.e		32	11.d	odd	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(33, [\chi])\).