Newform orbit 425.2.n.e

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

Newspace parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.39364208590\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
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 + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
49.1	−1.91681	+	1.91681i	0.977976	−	0.405091i		−	5.34834i		0		−1.09811	+	2.65108i	−0.544082	+	1.31353i	6.41814	+	6.41814i	−1.32898	+	1.32898i		0
49.2	−0.921271	+	0.921271i	−0.309218	+	0.128082i			0.302521i		0		0.166875	−	0.402872i	1.49424	−	3.60742i	−2.12124	−	2.12124i	−2.04211	+	2.04211i		0
49.3	−0.639117	+	0.639117i	2.66226	−	1.10274i			1.18306i		0		−0.996713	+	2.40628i	−0.278207	+	0.671652i	−2.03435	−	2.03435i	3.75027	−	3.75027i		0
49.4	−0.187572	+	0.187572i	−1.67148	+	0.692349i			1.92963i		0		0.183657	−	0.443388i	−1.88562	+	4.55230i	−0.737090	−	0.737090i	0.193173	−	0.193173i		0
49.5	0.917051	−	0.917051i	−1.69803	+	0.703348i			0.318036i		0		−0.912176	+	2.20219i	1.34200	−	3.23987i	2.12576	+	2.12576i	0.267297	−	0.267297i		0
49.6	1.33351	−	1.33351i	1.74560	−	0.723051i		−	1.55648i		0		1.36358	−	3.29196i	−0.128325	+	0.309803i	0.591431	+	0.591431i	0.402996	−	0.402996i		0
274.1	−1.71892	+	1.71892i	0.281370	+	0.679288i		−	3.90934i		0		−1.65129	−	0.683987i	−0.537508	−	0.222643i	3.28199	+	3.28199i	1.73906	−	1.73906i		0
274.2	−0.813283	+	0.813283i	−0.786634	−	1.89910i			0.677141i		0		2.18426	+	0.904752i	0.346882	+	0.143683i	−2.17727	−	2.17727i	−0.866476	+	0.866476i		0
274.3	−0.392996	+	0.392996i	0.958007	+	2.31283i			1.69111i		0		−1.28543	−	0.532441i	−3.72866	−	1.54446i	−1.45059	−	1.45059i	−2.31010	+	2.31010i		0
274.4	0.982785	−	0.982785i	−0.0424107	−	0.102388i			0.0682683i		0		−0.142306	−	0.0589452i	−1.58527	−	0.656642i	2.03266	+	2.03266i	2.11264	−	2.11264i		0
274.5	1.52941	−	1.52941i	1.06191	+	2.56367i		−	2.67820i		0		5.54499	+	2.29681i	2.90308	+	1.20249i	−1.03724	−	1.03724i	−3.32343	+	3.32343i		0
274.6	1.82721	−	1.82721i	−1.17935	−	2.84719i		−	4.67741i		0		−7.35734	−	3.04751i	2.60148	+	1.07757i	−4.89219	−	4.89219i	−4.59433	+	4.59433i		0
349.1	−1.71892	−	1.71892i	0.281370	−	0.679288i			3.90934i		0		−1.65129	+	0.683987i	−0.537508	+	0.222643i	3.28199	−	3.28199i	1.73906	+	1.73906i		0
349.2	−0.813283	−	0.813283i	−0.786634	+	1.89910i		−	0.677141i		0		2.18426	−	0.904752i	0.346882	−	0.143683i	−2.17727	+	2.17727i	−0.866476	−	0.866476i		0
349.3	−0.392996	−	0.392996i	0.958007	−	2.31283i		−	1.69111i		0		−1.28543	+	0.532441i	−3.72866	+	1.54446i	−1.45059	+	1.45059i	−2.31010	−	2.31010i		0
349.4	0.982785	+	0.982785i	−0.0424107	+	0.102388i		−	0.0682683i		0		−0.142306	+	0.0589452i	−1.58527	+	0.656642i	2.03266	−	2.03266i	2.11264	+	2.11264i		0
349.5	1.52941	+	1.52941i	1.06191	−	2.56367i			2.67820i		0		5.54499	−	2.29681i	2.90308	−	1.20249i	−1.03724	+	1.03724i	−3.32343	−	3.32343i		0
349.6	1.82721	+	1.82721i	−1.17935	+	2.84719i			4.67741i		0		−7.35734	+	3.04751i	2.60148	−	1.07757i	−4.89219	+	4.89219i	−4.59433	−	4.59433i		0
399.1	−1.91681	−	1.91681i	0.977976	+	0.405091i			5.34834i		0		−1.09811	−	2.65108i	−0.544082	−	1.31353i	6.41814	−	6.41814i	−1.32898	−	1.32898i		0
399.2	−0.921271	−	0.921271i	−0.309218	−	0.128082i		−	0.302521i		0		0.166875	+	0.402872i	1.49424	+	3.60742i	−2.12124	+	2.12124i	−2.04211	−	2.04211i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
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.n.e		24
5.b	even	2	1		425.2.n.d		24
5.c	odd	4	1		425.2.m.c	✓	24
5.c	odd	4	1		425.2.m.d	yes	24
17.d	even	8	1		425.2.n.d		24
85.k	odd	8	1		425.2.m.c	✓	24
85.m	even	8	1	inner	425.2.n.e		24
85.n	odd	8	1		425.2.m.d	yes	24
85.o	even	16	2		7225.2.a.bx		24
85.r	even	16	2		7225.2.a.cb		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
425.2.m.c	✓	24	5.c	odd	4	1
425.2.m.c	✓	24	85.k	odd	8	1
425.2.m.d	yes	24	5.c	odd	4	1
425.2.m.d	yes	24	85.n	odd	8	1
425.2.n.d		24	5.b	even	2	1
425.2.n.d		24	17.d	even	8	1
425.2.n.e		24	1.a	even	1	1	trivial
425.2.n.e		24	85.m	even	8	1	inner
7225.2.a.bx		24	85.o	even	16	2
7225.2.a.cb		24	85.r	even	16	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 + 90*T2^20 - 12*T2^19 + 100*T2^17 + 2351*T2^16 - 392*T2^15 + 72*T2^14 + 4456*T2^13 + 17604*T2^12 + 3824*T2^11 + 3224*T2^10 + 23720*T2^9 + 56111*T2^8 + 32464*T2^7 + 17112*T2^6 + 35584*T2^5 + 65814*T2^4 + 53060*T2^3 + 24200*T2^2 + 5500*T2 + 625