Newform orbit 22.14.c.a

• Label: 22.14.c.a
• Level: $22$
• Weight: $14$
• Character orbit: 22.c
• Analytic conductor: $23.591$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.5908043694\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 384 q^{2} + 2708 q^{3} - 24576 q^{4} + 32920 q^{5} + 47488 q^{6} - 509572 q^{7} + 1572864 q^{8} - 3517894 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	51.7771	−	37.6183i	−663.076	−	2040.74i	1265.73	−	3895.53i	18873.2	+	13712.2i	−111101.	−	80719.7i	−130921.	+	402934.i	−81007.0	−	249314.i	−2.43511e6	+	1.76921e6i	1.49303e6
3.2	51.7771	−	37.6183i	−417.662	−	1285.43i	1265.73	−	3895.53i	−34004.8	−	24705.9i	−69981.0	−	50844.2i	96600.4	−	297306.i	−81007.0	−	249314.i	−188057.	+	136631.i	−2.69006e6
3.3	51.7771	−	37.6183i	−252.702	−	777.736i	1265.73	−	3895.53i	25133.6	+	18260.6i	−42341.2	−	30762.7i	29224.9	−	89945.0i	−81007.0	−	249314.i	748819.	−	544049.i	1.98828e6
3.4	51.7771	−	37.6183i	346.581	+	1066.67i	1265.73	−	3895.53i	−24923.9	−	18108.3i	58071.1	+	42191.1i	−7979.10	+	24557.2i	−81007.0	−	249314.i	272175.	−	197747.i	−1.97169e6
3.5	51.7771	−	37.6183i	460.202	+	1416.35i	1265.73	−	3895.53i	46818.1	+	34015.4i	77108.7	+	56022.7i	−157481.	+	484676.i	−81007.0	−	249314.i	−504441.	+	366498.i	3.70370e6
3.6	51.7771	−	37.6183i	461.283	+	1419.68i	1265.73	−	3895.53i	−3259.92	−	2368.47i	77289.8	+	56154.3i	80603.6	−	248072.i	−81007.0	−	249314.i	−512880.	+	372629.i	−257887.
5.1	−19.7771	−	60.8676i	−1602.93	−	1164.60i	−3313.73	+	2407.57i	100.214	−	308.427i	−39185.0	+	120599.i	51623.9	−	37507.0i	212079.	+	154084.i	720428.	+	2.21725e6i	−20755.1
5.2	−19.7771	−	60.8676i	−351.775	−	255.580i	−3313.73	+	2407.57i	−3087.88	+	9503.52i	−8599.44	+	26466.3i	327454.	−	237910.i	212079.	+	154084.i	−434248.	−	1.33648e6i	639526.
5.3	−19.7771	−	60.8676i	−269.653	−	195.914i	−3313.73	+	2407.57i	−21195.1	+	65231.8i	−6591.88	+	20287.7i	−348859.	+	253461.i	212079.	+	154084.i	−458343.	−	1.41063e6i	4.38968e6
5.4	−19.7771	−	60.8676i	719.209	+	522.536i	−3313.73	+	2407.57i	552.241	−	1699.62i	17581.7	−	54110.8i	−85138.9	+	61857.0i	212079.	+	154084.i	−248455.	−	764667.i	−114374.
5.5	−19.7771	−	60.8676i	950.343	+	690.465i	−3313.73	+	2407.57i	20485.5	−	63047.8i	23231.9	−	71500.5i	4712.51	−	3423.84i	212079.	+	154084.i	−66262.0	−	203934.i	−4.24271e6
5.6	−19.7771	−	60.8676i	1974.18	+	1434.33i	−3313.73	+	2407.57i	−9031.32	+	27795.5i	48260.5	−	148531.i	−114626.	+	83280.8i	212079.	+	154084.i	1.34743e6	+	4.14695e6i	1.87046e6
9.1	−19.7771	+	60.8676i	−1602.93	+	1164.60i	−3313.73	−	2407.57i	100.214	+	308.427i	−39185.0	−	120599.i	51623.9	+	37507.0i	212079.	−	154084.i	720428.	−	2.21725e6i	−20755.1
9.2	−19.7771	+	60.8676i	−351.775	+	255.580i	−3313.73	−	2407.57i	−3087.88	−	9503.52i	−8599.44	−	26466.3i	327454.	+	237910.i	212079.	−	154084.i	−434248.	+	1.33648e6i	639526.
9.3	−19.7771	+	60.8676i	−269.653	+	195.914i	−3313.73	−	2407.57i	−21195.1	−	65231.8i	−6591.88	−	20287.7i	−348859.	−	253461.i	212079.	−	154084.i	−458343.	+	1.41063e6i	4.38968e6
9.4	−19.7771	+	60.8676i	719.209	−	522.536i	−3313.73	−	2407.57i	552.241	+	1699.62i	17581.7	+	54110.8i	−85138.9	−	61857.0i	212079.	−	154084.i	−248455.	+	764667.i	−114374.
9.5	−19.7771	+	60.8676i	950.343	−	690.465i	−3313.73	−	2407.57i	20485.5	+	63047.8i	23231.9	+	71500.5i	4712.51	+	3423.84i	212079.	−	154084.i	−66262.0	+	203934.i	−4.24271e6
9.6	−19.7771	+	60.8676i	1974.18	−	1434.33i	−3313.73	−	2407.57i	−9031.32	−	27795.5i	48260.5	+	148531.i	−114626.	−	83280.8i	212079.	−	154084.i	1.34743e6	−	4.14695e6i	1.87046e6
15.1	51.7771	+	37.6183i	−663.076	+	2040.74i	1265.73	+	3895.53i	18873.2	−	13712.2i	−111101.	+	80719.7i	−130921.	−	402934.i	−81007.0	+	249314.i	−2.43511e6	−	1.76921e6i	1.49303e6
15.2	51.7771	+	37.6183i	−417.662	+	1285.43i	1265.73	+	3895.53i	−34004.8	+	24705.9i	−69981.0	+	50844.2i	96600.4	+	297306.i	−81007.0	+	249314.i	−188057.	−	136631.i	−2.69006e6

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	22.14.c.a	✓	24
11.c	even	5	1	inner	22.14.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
22.14.c.a	✓	24	1.a	even	1	1	trivial
22.14.c.a	✓	24	11.c	even	5	1	inner