Newform orbit 432.2.be.c

• Label: 432.2.be.c
• Level: $432$
• Weight: $2$
• Character orbit: 432.be
• Analytic conductor: $3.450$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.44953736732\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(6\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1		0		−1.50778	−	0.852402i		0		−2.12767	+	0.375166i		0		2.50142	−	2.98107i		0		1.54682	+	2.57047i		0
47.2		0		−1.36628	+	1.06456i		0		1.83017	−	0.322709i		0		0.441545	−	0.526213i		0		0.733433	−	2.90896i		0
47.3		0		−0.721706	−	1.57453i		0		0.976679	−	0.172215i		0		−3.12803	+	3.72784i		0		−1.95828	+	2.27269i		0
47.4		0		0.939092	−	1.45537i		0		−1.07086	+	0.188822i		0		0.0466102	−	0.0555478i		0		−1.23621	−	2.73346i		0
47.5		0		1.59623	+	0.672336i		0		4.18690	−	0.738263i		0		−1.26944	+	1.51285i		0		2.09593	+	2.14641i		0
47.6		0		1.65284	+	0.517813i		0		−2.52917	+	0.445961i		0		1.40789	−	1.67786i		0		2.46374	+	1.71172i		0
95.1		0		−1.70424	+	0.309120i		0		−1.45395	+	1.73275i		0		1.49276	−	4.10134i		0		2.80889	−	1.05363i		0
95.2		0		−1.63553	−	0.570126i		0		2.34697	−	2.79701i		0		−0.550750	+	1.51317i		0		2.34991	+	1.86492i		0
95.3		0		−0.536320	+	1.64692i		0		−1.32159	+	1.57501i		0		−1.34711	+	3.70114i		0		−2.42472	−	1.76656i		0
95.4		0		−0.249148	−	1.71404i		0		−1.47612	+	1.75917i		0		−0.590654	+	1.62281i		0		−2.87585	+	0.854099i		0
95.5		0		1.19574	+	1.25308i		0		0.311559	−	0.371302i		0		0.958275	−	2.63284i		0		−0.140409	+	2.99671i		0
95.6		0		1.22376	−	1.22573i		0		1.15344	−	1.37462i		0		0.0374696	−	0.102947i		0		−0.00480931	−	3.00000i		0
191.1		0		−1.70424	−	0.309120i		0		−1.45395	−	1.73275i		0		1.49276	+	4.10134i		0		2.80889	+	1.05363i		0
191.2		0		−1.63553	+	0.570126i		0		2.34697	+	2.79701i		0		−0.550750	−	1.51317i		0		2.34991	−	1.86492i		0
191.3		0		−0.536320	−	1.64692i		0		−1.32159	−	1.57501i		0		−1.34711	−	3.70114i		0		−2.42472	+	1.76656i		0
191.4		0		−0.249148	+	1.71404i		0		−1.47612	−	1.75917i		0		−0.590654	−	1.62281i		0		−2.87585	−	0.854099i		0
191.5		0		1.19574	−	1.25308i		0		0.311559	+	0.371302i		0		0.958275	+	2.63284i		0		−0.140409	−	2.99671i		0
191.6		0		1.22376	+	1.22573i		0		1.15344	+	1.37462i		0		0.0374696	+	0.102947i		0		−0.00480931	+	3.00000i		0
239.1		0		−1.50778	+	0.852402i		0		−2.12767	−	0.375166i		0		2.50142	+	2.98107i		0		1.54682	−	2.57047i		0
239.2		0		−1.36628	−	1.06456i		0		1.83017	+	0.322709i		0		0.441545	+	0.526213i		0		0.733433	+	2.90896i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
108.l	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	432.2.be.c	yes	36
4.b	odd	2	1		432.2.be.b	✓	36
27.f	odd	18	1		432.2.be.b	✓	36
108.l	even	18	1	inner	432.2.be.c	yes	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
432.2.be.b	✓	36	4.b	odd	2	1
432.2.be.b	✓	36	27.f	odd	18	1
432.2.be.c	yes	36	1.a	even	1	1	trivial
432.2.be.c	yes	36	108.l	even	18	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(432, [\chi])\):

T5^36 - 3*T5^35 + 9*T5^34 - 33*T5^33 - 108*T5^31 - 2493*T5^30 + 2277*T5^29 + 10935*T5^28 - 2952*T5^27 + 169857*T5^26 + 1473687*T5^25 + 3988251*T5^24 + 5571072*T5^23 + 21695445*T5^22 + 52419744*T5^21 - 40406283*T5^20 - 395074827*T5^19 - 410772249*T5^18 + 728806734*T5^17 + 595177713*T5^16 - 2869259598*T5^15 - 2593039149*T5^14 + 9825163110*T5^13 + 20842273782*T5^12 + 6777318600*T5^11 - 618190542*T5^10 - 15193153395*T5^9 - 8579305755*T5^8 - 7846770834*T5^7 - 33302928141*T5^6 + 20676363102*T5^5 + 27541205928*T5^4 - 8394149232*T5^3 + 7486363440*T5^2 - 1490169312*T5 + 1847624256

T7^36 + 81*T7^32 - 351*T7^31 - 6399*T7^30 + 19521*T7^29 - 29322*T7^28 - 28431*T7^27 + 269487*T7^26 - 3623616*T7^25 + 36709524*T7^24 - 69289992*T7^23 + 1750329*T7^22 + 165315330*T7^21 - 635767461*T7^20 - 1286292798*T7^19 - 2071352169*T7^18 + 11892921309*T7^17 + 12079949175*T7^16 - 1212866460*T7^15 + 56784825144*T7^14 + 193913530524*T7^13 + 635472642465*T7^12 + 173002704984*T7^11 - 377874332415*T7^10 - 897025641192*T7^9 - 386523593739*T7^8 + 1376567353161*T7^7 - 264127771323*T7^6 - 785115858294*T7^5 + 674560187064*T7^4 - 110454697440*T7^3 + 14310643248*T7^2 - 867311712*T7 + 34012224