Newform orbit 425.2.m.e

• Label: 425.2.m.e
• Level: $425$
• Weight: $2$
• Character orbit: 425.m
• Analytic conductor: $3.394$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.39364208590\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{8})\)
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
26.1	−1.48843	+	1.48843i	−1.66813	−	0.690961i		−	2.43082i		0		3.51133	−	1.45444i	−1.02689	−	2.47912i	0.641241	+	0.641241i	0.183901	+	0.183901i		0
26.2	−0.672981	+	0.672981i	2.28645	+	0.947078i			1.09419i		0		−2.17610	+	0.901371i	0.204115	+	0.492777i	−2.08233	−	2.08233i	2.20957	+	2.20957i		0
26.3	−0.352960	+	0.352960i	−0.158243	−	0.0655465i			1.75084i		0		0.0789888	−	0.0327182i	−1.48214	−	3.57820i	−1.32390	−	1.32390i	−2.10058	−	2.10058i		0
26.4	0.352960	−	0.352960i	0.158243	+	0.0655465i			1.75084i		0		0.0789888	−	0.0327182i	1.48214	+	3.57820i	1.32390	+	1.32390i	−2.10058	−	2.10058i		0
26.5	0.672981	−	0.672981i	−2.28645	−	0.947078i			1.09419i		0		−2.17610	+	0.901371i	−0.204115	−	0.492777i	2.08233	+	2.08233i	2.20957	+	2.20957i		0
26.6	1.48843	−	1.48843i	1.66813	+	0.690961i		−	2.43082i		0		3.51133	−	1.45444i	1.02689	+	2.47912i	−0.641241	−	0.641241i	0.183901	+	0.183901i		0
76.1	−1.63043	+	1.63043i	−0.718554	+	1.73474i		−	3.31660i		0		−1.65683	−	3.99993i	1.42808	−	0.591528i	2.14663	+	2.14663i	−0.371694	−	0.371694i		0
76.2	−1.23200	+	1.23200i	0.229112	−	0.553124i		−	1.03565i		0		0.399184	+	0.963715i	−0.958968	+	0.397218i	−1.18808	−	1.18808i	1.86787	+	1.86787i		0
76.3	−0.176012	+	0.176012i	−0.629010	+	1.51856i			1.93804i		0		−0.156572	−	0.377999i	−1.32215	+	0.547653i	−0.693142	−	0.693142i	0.210935	+	0.210935i		0
76.4	0.176012	−	0.176012i	0.629010	−	1.51856i			1.93804i		0		−0.156572	−	0.377999i	1.32215	−	0.547653i	0.693142	+	0.693142i	0.210935	+	0.210935i		0
76.5	1.23200	−	1.23200i	−0.229112	+	0.553124i		−	1.03565i		0		0.399184	+	0.963715i	0.958968	−	0.397218i	1.18808	+	1.18808i	1.86787	+	1.86787i		0
76.6	1.63043	−	1.63043i	0.718554	−	1.73474i		−	3.31660i		0		−1.65683	−	3.99993i	−1.42808	+	0.591528i	−2.14663	−	2.14663i	−0.371694	−	0.371694i		0
151.1	−1.63043	−	1.63043i	−0.718554	−	1.73474i			3.31660i		0		−1.65683	+	3.99993i	1.42808	+	0.591528i	2.14663	−	2.14663i	−0.371694	+	0.371694i		0
151.2	−1.23200	−	1.23200i	0.229112	+	0.553124i			1.03565i		0		0.399184	−	0.963715i	−0.958968	−	0.397218i	−1.18808	+	1.18808i	1.86787	−	1.86787i		0
151.3	−0.176012	−	0.176012i	−0.629010	−	1.51856i		−	1.93804i		0		−0.156572	+	0.377999i	−1.32215	−	0.547653i	−0.693142	+	0.693142i	0.210935	−	0.210935i		0
151.4	0.176012	+	0.176012i	0.629010	+	1.51856i		−	1.93804i		0		−0.156572	+	0.377999i	1.32215	+	0.547653i	0.693142	−	0.693142i	0.210935	−	0.210935i		0
151.5	1.23200	+	1.23200i	−0.229112	−	0.553124i			1.03565i		0		0.399184	−	0.963715i	0.958968	+	0.397218i	1.18808	−	1.18808i	1.86787	−	1.86787i		0
151.6	1.63043	+	1.63043i	0.718554	+	1.73474i			3.31660i		0		−1.65683	+	3.99993i	−1.42808	−	0.591528i	−2.14663	+	2.14663i	−0.371694	+	0.371694i		0
376.1	−1.48843	−	1.48843i	−1.66813	+	0.690961i			2.43082i		0		3.51133	+	1.45444i	−1.02689	+	2.47912i	0.641241	−	0.641241i	0.183901	−	0.183901i		0
376.2	−0.672981	−	0.672981i	2.28645	−	0.947078i		−	1.09419i		0		−2.17610	−	0.901371i	0.204115	−	0.492777i	−2.08233	+	2.08233i	2.20957	−	2.20957i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
17.d	even	8	1	inner
85.m	even	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	425.2.m.e		24
5.b	even	2	1	inner	425.2.m.e		24
5.c	odd	4	2		85.2.m.a	✓	24
15.e	even	4	2		765.2.bh.b		24
17.d	even	8	1	inner	425.2.m.e		24
17.e	odd	16	2		7225.2.a.by		24
85.k	odd	8	1		85.2.m.a	✓	24
85.m	even	8	1	inner	425.2.m.e		24
85.n	odd	8	1		85.2.m.a	✓	24
85.o	even	16	2		1445.2.b.i		24
85.p	odd	16	2		7225.2.a.by		24
85.r	even	16	2		1445.2.b.i		24
255.v	even	8	1		765.2.bh.b		24
255.ba	even	8	1		765.2.bh.b		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
85.2.m.a	✓	24	5.c	odd	4	2
85.2.m.a	✓	24	85.k	odd	8	1
85.2.m.a	✓	24	85.n	odd	8	1
425.2.m.e		24	1.a	even	1	1	trivial
425.2.m.e		24	5.b	even	2	1	inner
425.2.m.e		24	17.d	even	8	1	inner
425.2.m.e		24	85.m	even	8	1	inner
765.2.bh.b		24	15.e	even	4	2
765.2.bh.b		24	255.v	even	8	1
765.2.bh.b		24	255.ba	even	8	1
1445.2.b.i		24	85.o	even	16	2
1445.2.b.i		24	85.r	even	16	2
7225.2.a.by		24	17.e	odd	16	2
7225.2.a.by		24	85.p	odd	16	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 58T_{2}^{20} + 1047T_{2}^{16} + 6000T_{2}^{12} + 4587T_{2}^{8} + 278T_{2}^{4} + 1 \) acting on \(S_{2}^{\mathrm{new}}(425, [\chi])\).