Newform orbit 33.14.d.b

• Label: 33.14.d.b
• Level: $33$
• Weight: $14$
• Character orbit: 33.d
• Analytic conductor: $35.386$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(35.3862065541\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 696 q^{3} + 212988 q^{4} - 421992 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−170.839			−925.430	−	859.013i	20993.9					8677.01i	158099.	+	146753.i			329762.i	−2.18706e6			118517.	+	1.58991e6i		−	1.48237e6i
32.2	−170.839			−925.430	+	859.013i	20993.9				−	8677.01i	158099.	−	146753.i		−	329762.i	−2.18706e6			118517.	−	1.58991e6i			1.48237e6i
32.3	−163.385			1052.54	−	697.490i	18502.6					19154.3i	−171968.	+	113959.i			232054.i	−1.68459e6			621338.	−	1.46827e6i		−	3.12952e6i
32.4	−163.385			1052.54	+	697.490i	18502.6				−	19154.3i	−171968.	−	113959.i		−	232054.i	−1.68459e6			621338.	+	1.46827e6i			3.12952e6i
32.5	−146.356			−138.713	−	1255.02i	13228.2					28563.5i	20301.6	+	183681.i		−	547807.i	−737084.			−1.55584e6	+	348176.i		−	4.18045e6i
32.6	−146.356			−138.713	+	1255.02i	13228.2				−	28563.5i	20301.6	−	183681.i			547807.i	−737084.			−1.55584e6	−	348176.i			4.18045e6i
32.7	−139.894			486.512	−	1165.17i	11378.3				−	64265.5i	−68060.1	+	163001.i		−	236833.i	−445747.			−1.12094e6	−	1.13374e6i			8.99035e6i
32.8	−139.894			486.512	+	1165.17i	11378.3					64265.5i	−68060.1	−	163001.i			236833.i	−445747.			−1.12094e6	+	1.13374e6i		−	8.99035e6i
32.9	−131.377			−1221.71	−	318.993i	9068.04				−	56962.3i	160505.	+	41908.4i			78540.7i	−115092.			1.39081e6	+	779430.i			7.48357e6i
32.10	−131.377			−1221.71	+	318.993i	9068.04					56962.3i	160505.	−	41908.4i		−	78540.7i	−115092.			1.39081e6	−	779430.i		−	7.48357e6i
32.11	−103.446			1260.72	+	70.0278i	2509.08				−	37467.6i	−130417.	−	7244.09i			159657.i	587875.			1.58452e6	+	176571.i			3.87587e6i
32.12	−103.446			1260.72	−	70.0278i	2509.08					37467.6i	−130417.	+	7244.09i		−	159657.i	587875.			1.58452e6	−	176571.i		−	3.87587e6i
32.13	−100.350			304.827	+	1225.32i	1878.02				−	6402.02i	−30589.3	−	122960.i		−	527405.i	633604.			−1.40848e6	+	747020.i			642439.i
32.14	−100.350			304.827	−	1225.32i	1878.02					6402.02i	−30589.3	+	122960.i			527405.i	633604.			−1.40848e6	−	747020.i		−	642439.i
32.15	−99.4888			−899.927	−	885.694i	1706.02					14437.0i	89532.6	+	88116.7i		−	7425.56i	645282.			25413.7	+	1.59412e6i		−	1.43632e6i
32.16	−99.4888			−899.927	+	885.694i	1706.02				−	14437.0i	89532.6	−	88116.7i			7425.56i	645282.			25413.7	−	1.59412e6i			1.43632e6i
32.17	−53.3141			696.893	+	1052.93i	−5349.61				−	39833.9i	−37154.2	−	56136.0i			214863.i	721958.			−623002.	+	1.46756e6i			2.12371e6i
32.18	−53.3141			696.893	−	1052.93i	−5349.61					39833.9i	−37154.2	+	56136.0i		−	214863.i	721958.			−623002.	−	1.46756e6i		−	2.12371e6i
32.19	−42.4148			−1228.16	−	293.180i	−6392.98				−	21829.9i	52092.0	+	12435.2i		−	493447.i	618619.			1.42241e6	+	720142.i			925910.i
32.20	−42.4148			−1228.16	+	293.180i	−6392.98					21829.9i	52092.0	−	12435.2i			493447.i	618619.			1.42241e6	−	720142.i		−	925910.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.b	odd	2	1	inner
33.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	33.14.d.b	✓	48
3.b	odd	2	1	inner	33.14.d.b	✓	48
11.b	odd	2	1	inner	33.14.d.b	✓	48
33.d	even	2	1	inner	33.14.d.b	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
33.14.d.b	✓	48	1.a	even	1	1	trivial
33.14.d.b	✓	48	3.b	odd	2	1	inner
33.14.d.b	✓	48	11.b	odd	2	1	inner
33.14.d.b	✓	48	33.d	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 - 151551*T2^22 + 9967864638*T2^20 - 373579513970400*T2^18 + 8807300169430275936*T2^16 - 136055120143513142301696*T2^14 + 1391660379335811783798079488*T2^12 - 9316764895698451439680436305920*T2^10 + 39542512423328769482489417479225344*T2^8 - 101056527168868776213665170897036640256*T2^6 + 145465784456871712684977243519551715409920*T2^4 - 105001486613327609947049794017683939367321600*T2^2 + 28095710982806733938529510890309069907689472000