Newform orbit 495.2.bs.a

• Label: 495.2.bs.a
• Level: $495$
• Weight: $2$
• Character orbit: 495.bs
• Analytic conductor: $3.953$
• Analytic rank: $0$
• Dimension: $1088$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bs (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.95259490005\)
Analytic rank:	\(0\)
Dimension:	\(1088\)
Relative dimension:	\(68\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1088 q - 10 q^{2} - 14 q^{3} - 6 q^{5} - 40 q^{6} - 10 q^{7} - 40 q^{8}+O(q^{10}) \)

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	−1.01049	+	2.63243i	−1.16040	−	1.28587i	−4.42228	−	3.98184i	−0.701901	−	2.12305i	4.55754	−	1.75531i	0.285761	−	0.185575i	9.92584	−	5.05747i	−0.306933	+	2.98426i	6.29804	+	0.297626i
7.2	−0.989542	+	2.57784i	1.72283	+	0.178491i	−4.17980	−	3.76351i	−0.409307	+	2.19829i	−2.16493	+	4.26456i	2.60351	−	1.69074i	8.91725	−	4.54356i	2.93628	+	0.615019i	−5.26182	−	3.23043i
7.3	−0.938997	+	2.44617i	−0.741205	+	1.56544i	−3.61575	−	3.25563i	−2.14163	+	0.642981i	−3.13335	−	3.28306i	−3.33465	+	2.16555i	6.68977	−	3.40861i	−1.90123	−	2.32063i	0.438142	−	5.84255i
7.4	−0.895280	+	2.33229i	−0.954306	+	1.44544i	−3.15174	−	2.83784i	1.36995	−	1.76727i	−2.51681	−	3.51979i	1.55209	−	1.00794i	4.98848	−	2.54176i	−1.17860	−	2.75879i	2.89528	+	4.77731i
7.5	−0.874266	+	2.27754i	−1.69695	+	0.346942i	−2.93656	−	2.64409i	−0.218470	+	2.22537i	0.693408	−	4.16819i	2.22055	−	1.44204i	4.24202	−	2.16142i	2.75926	−	1.17749i	−4.87737	−	2.44314i
7.6	−0.851826	+	2.21908i	1.58893	−	0.689423i	−2.71243	−	2.44229i	−2.07945	−	0.822126i	0.176395	+	4.11324i	−1.65908	+	1.07742i	3.49439	−	1.78048i	2.04939	−	2.19089i	3.59570	−	3.91416i
7.7	−0.834127	+	2.17298i	−1.72681	−	0.134696i	−2.53976	−	2.28681i	2.10441	+	0.755961i	1.73307	−	3.63995i	−2.12480	+	1.37986i	2.93991	−	1.49796i	2.96371	+	0.465189i	−3.39803	+	3.94225i
7.8	−0.816513	+	2.12709i	1.14507	+	1.29955i	−2.37153	−	2.13533i	0.278325	−	2.21868i	−3.69922	+	1.37456i	−2.06419	+	1.34050i	2.41825	−	1.23216i	−0.377651	+	2.97613i	4.49207	+	2.40360i
7.9	−0.799946	+	2.08393i	1.72661	+	0.137190i	−2.21656	−	1.99580i	2.07276	−	0.838844i	−1.66709	+	3.48839i	0.244996	−	0.159102i	1.95445	−	0.995842i	2.96236	+	0.473749i	0.0899956	+	4.99052i
7.10	−0.799872	+	2.08374i	0.0995422	−	1.72919i	−2.21588	−	1.99519i	−2.07992	+	0.820927i	3.52355	+	1.59055i	0.906263	−	0.588534i	1.95244	−	0.994820i	−2.98018	−	0.344254i	−0.0469255	−	4.99065i
7.11	−0.795884	+	2.07335i	0.490034	−	1.66128i	−2.17905	−	1.96203i	2.22591	−	0.212931i	3.05441	+	2.33820i	3.61252	−	2.34600i	1.84464	−	0.939891i	−2.51973	−	1.62817i	−1.33008	+	4.78455i
7.12	−0.680279	+	1.77219i	−1.70442	−	0.308163i	−1.19158	−	1.07290i	−1.94984	−	1.09459i	1.70560	−	2.81091i	2.38040	−	1.54585i	−0.670753	+	0.341766i	2.81007	+	1.05048i	3.26626	−	2.71085i
7.13	−0.677288	+	1.76440i	0.513453	+	1.65420i	−1.16808	−	1.05175i	−2.03489	+	0.926937i	−3.26641	−	0.214433i	1.34541	−	0.873719i	−0.721042	+	0.367389i	−2.47273	+	1.69870i	−0.257276	−	4.21816i
7.14	−0.669490	+	1.74408i	1.23441	−	1.21500i	−1.10731	−	0.997029i	0.461660	+	2.18789i	1.29264	+	2.96634i	−3.08743	+	2.00500i	−0.848859	+	0.432515i	0.0475413	−	2.99962i	−4.12494	−	0.659599i
7.15	−0.645470	+	1.68151i	1.28974	+	1.15610i	−0.924547	−	0.832466i	0.320426	+	2.21299i	−2.77648	+	1.42248i	−2.46679	+	1.60195i	−1.21309	+	0.618099i	0.326861	+	2.98214i	−3.92799	−	0.889621i
7.16	−0.633120	+	1.64934i	−1.15714	−	1.28881i	−0.833175	−	0.750194i	1.73204	−	1.41422i	2.85829	−	1.09254i	−1.34188	+	0.871426i	−1.38342	+	0.704887i	−0.322059	+	2.98266i	1.23594	+	3.75209i
7.17	−0.612457	+	1.59551i	−0.0463442	+	1.73143i	−0.684244	−	0.616096i	1.76079	+	1.37827i	−2.73412	−	1.13437i	3.90660	−	2.53698i	−1.64344	+	0.837373i	−2.99570	−	0.160483i	−3.27744	+	1.96522i
7.18	−0.596739	+	1.55456i	−0.975589	+	1.43116i	−0.574264	−	0.517069i	−0.0219856	−	2.23596i	−1.64265	−	2.37064i	0.507510	−	0.329581i	−1.82083	+	0.927760i	−1.09645	−	2.79245i	3.48905	+	1.30011i
7.19	−0.546979	+	1.42493i	0.202141	−	1.72021i	−0.244947	−	0.220551i	−0.227794	−	2.22443i	2.34062	+	1.22896i	−3.24085	+	2.10464i	−2.27165	+	1.15746i	−2.91828	−	0.695452i	3.29426	+	0.892128i
7.20	−0.487438	+	1.26982i	−1.03484	+	1.38892i	0.111446	+	0.100347i	1.91083	+	1.16134i	−1.25926	−	1.99107i	−3.46965	+	2.25321i	−2.60557	+	1.32760i	−0.858211	−	2.87463i	−2.40610	+	1.86033i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
9.c	even	3	1	inner
11.d	odd	10	1	inner
45.k	odd	12	1	inner
55.l	even	20	1	inner
99.o	odd	30	1	inner
495.bs	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	495.2.bs.a	✓	1088
5.c	odd	4	1	inner	495.2.bs.a	✓	1088
9.c	even	3	1	inner	495.2.bs.a	✓	1088
11.d	odd	10	1	inner	495.2.bs.a	✓	1088
45.k	odd	12	1	inner	495.2.bs.a	✓	1088
55.l	even	20	1	inner	495.2.bs.a	✓	1088
99.o	odd	30	1	inner	495.2.bs.a	✓	1088
495.bs	even	60	1	inner	495.2.bs.a	✓	1088

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
495.2.bs.a	✓	1088	1.a	even	1	1	trivial
495.2.bs.a	✓	1088	5.c	odd	4	1	inner
495.2.bs.a	✓	1088	9.c	even	3	1	inner
495.2.bs.a	✓	1088	11.d	odd	10	1	inner
495.2.bs.a	✓	1088	45.k	odd	12	1	inner
495.2.bs.a	✓	1088	55.l	even	20	1	inner
495.2.bs.a	✓	1088	99.o	odd	30	1	inner
495.2.bs.a	✓	1088	495.bs	even	60	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(495, [\chi])\).