Newform orbit 5.25.c.a

• Label: 5.25.c.a
• Level: $5$
• Weight: $25$
• Character orbit: 5.c
• Analytic conductor: $18.248$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.2483576129\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Relative dimension:	\(11\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 2 q^{2} - 434562 q^{3} - 413381810 q^{5} - 1921066536 q^{6} + 9255727198 q^{7} + 133568743140 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−5471.99	−	5471.99i	297236.	−	297236.i			4.31081e7i	−2.31171e8	+	7.85158e7i	−3.25294e9			5.07083e9	+	5.07083e9i	1.44082e11	−	1.44082e11i			1.05731e11i	1.69460e12	+	8.35326e11i
2.2	−4581.98	−	4581.98i	−719594.	+	719594.i			2.52119e7i	2.56648e7	−	2.42788e8i	6.59434e9			2.82041e8	+	2.82041e8i	3.86475e10	−	3.86475e10i		−	7.53203e11i	−1.23005e12	+	9.94854e11i
2.3	−3489.17	−	3489.17i	145240.	−	145240.i			7.57135e6i	2.43739e8	−	1.40064e7i	−1.01354e9			−1.00331e9	−	1.00331e9i	−3.21208e10	+	3.21208e10i			2.40240e11i	−8.99315e11	−	8.01574e11i
2.4	−2131.70	−	2131.70i	−273844.	+	273844.i		−	7.68892e6i	−1.29596e8	+	2.06904e8i	1.16751e9			−2.53345e8	−	2.53345e8i	−5.21545e10	+	5.21545e10i			1.32449e11i	7.17319e11	−	1.64798e11i
2.5	−1612.12	−	1612.12i	590974.	−	590974.i		−	1.15794e7i	−1.30653e8	−	2.06238e8i	−1.90544e9			−1.08814e10	−	1.08814e10i	−4.57142e10	+	4.57142e10i		−	4.16072e11i	−1.21852e11	+	5.43109e11i
2.6	761.183	+	761.183i	−196404.	+	196404.i		−	1.56184e7i	−9.44904e7	−	2.25114e8i	−2.98999e8			8.18922e9	+	8.18922e9i	2.46590e10	−	2.46590e10i			2.05281e11i	9.94283e10	−	2.43277e11i
2.7	1287.24	+	1287.24i	508337.	−	508337.i		−	1.34632e7i	1.18556e8	+	2.13422e8i	1.30870e9			1.40042e10	+	1.40042e10i	3.89267e10	−	3.89267e10i		−	2.34383e11i	−1.22115e11	+	4.27336e11i
2.8	1951.95	+	1951.95i	−473102.	+	473102.i		−	9.15696e6i	2.33690e8	+	7.06647e7i	−1.84695e9			−1.38559e10	−	1.38559e10i	5.06223e10	−	5.06223e10i		−	1.65221e11i	3.18218e11	+	5.94087e11i
2.9	3633.41	+	3633.41i	274294.	−	274294.i			9.62617e6i	−2.24863e8	+	9.50861e7i	1.99325e9			−1.65601e10	−	1.65601e10i	2.59827e10	−	2.59827e10i			1.31955e11i	−1.16251e12	−	4.71532e11i
2.10	4742.86	+	4742.86i	208672.	−	208672.i			2.82122e7i	1.76833e8	−	1.68329e8i	1.97940e9			3.43548e9	+	3.43548e9i	−5.42347e10	+	5.42347e10i			1.95342e11i	1.63706e12	+	4.03332e10i
2.11	4909.30	+	4909.30i	−579090.	+	579090.i			3.14253e7i	−1.94400e8	+	1.47693e8i	−5.68586e9			1.62002e10	+	1.62002e10i	−7.19120e10	+	7.19120e10i		−	3.88262e11i	−1.67944e12	−	2.29300e11i
3.1	−5471.99	+	5471.99i	297236.	+	297236.i		−	4.31081e7i	−2.31171e8	−	7.85158e7i	−3.25294e9			5.07083e9	−	5.07083e9i	1.44082e11	+	1.44082e11i		−	1.05731e11i	1.69460e12	−	8.35326e11i
3.2	−4581.98	+	4581.98i	−719594.	−	719594.i		−	2.52119e7i	2.56648e7	+	2.42788e8i	6.59434e9			2.82041e8	−	2.82041e8i	3.86475e10	+	3.86475e10i			7.53203e11i	−1.23005e12	−	9.94854e11i
3.3	−3489.17	+	3489.17i	145240.	+	145240.i		−	7.57135e6i	2.43739e8	+	1.40064e7i	−1.01354e9			−1.00331e9	+	1.00331e9i	−3.21208e10	−	3.21208e10i		−	2.40240e11i	−8.99315e11	+	8.01574e11i
3.4	−2131.70	+	2131.70i	−273844.	−	273844.i			7.68892e6i	−1.29596e8	−	2.06904e8i	1.16751e9			−2.53345e8	+	2.53345e8i	−5.21545e10	−	5.21545e10i		−	1.32449e11i	7.17319e11	+	1.64798e11i
3.5	−1612.12	+	1612.12i	590974.	+	590974.i			1.15794e7i	−1.30653e8	+	2.06238e8i	−1.90544e9			−1.08814e10	+	1.08814e10i	−4.57142e10	−	4.57142e10i			4.16072e11i	−1.21852e11	−	5.43109e11i
3.6	761.183	−	761.183i	−196404.	−	196404.i			1.56184e7i	−9.44904e7	+	2.25114e8i	−2.98999e8			8.18922e9	−	8.18922e9i	2.46590e10	+	2.46590e10i		−	2.05281e11i	9.94283e10	+	2.43277e11i
3.7	1287.24	−	1287.24i	508337.	+	508337.i			1.34632e7i	1.18556e8	−	2.13422e8i	1.30870e9			1.40042e10	−	1.40042e10i	3.89267e10	+	3.89267e10i			2.34383e11i	−1.22115e11	−	4.27336e11i
3.8	1951.95	−	1951.95i	−473102.	−	473102.i			9.15696e6i	2.33690e8	−	7.06647e7i	−1.84695e9			−1.38559e10	+	1.38559e10i	5.06223e10	+	5.06223e10i			1.65221e11i	3.18218e11	−	5.94087e11i
3.9	3633.41	−	3633.41i	274294.	+	274294.i		−	9.62617e6i	−2.24863e8	−	9.50861e7i	1.99325e9			−1.65601e10	+	1.65601e10i	2.59827e10	+	2.59827e10i		−	1.31955e11i	−1.16251e12	+	4.71532e11i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5.25.c.a	✓	22
5.b	even	2	1		25.25.c.b		22
5.c	odd	4	1	inner	5.25.c.a	✓	22
5.c	odd	4	1		25.25.c.b		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5.25.c.a	✓	22	1.a	even	1	1	trivial
5.25.c.a	✓	22	5.c	odd	4	1	inner
25.25.c.b		22	5.b	even	2	1
25.25.c.b		22	5.c	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{25}^{\mathrm{new}}(5, [\chi])\).