Newform orbit 300.5.c.e

• Label: 300.5.c.e
• Level: $300$
• Weight: $5$
• Character orbit: 300.c
• Analytic conductor: $31.011$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(31.0109889252\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 14 q^{4} - 18 q^{6} - 648 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
151.1	−3.91324	−	0.828581i			5.19615i	14.6269	+	6.48488i		0		4.30543	−	20.3338i			67.1774i	−51.8654	−	37.4965i	−27.0000				0
151.2	−3.91324	+	0.828581i		−	5.19615i	14.6269	−	6.48488i		0		4.30543	+	20.3338i		−	67.1774i	−51.8654	+	37.4965i	−27.0000				0
151.3	−3.87582	−	0.988963i		−	5.19615i	14.0439	+	7.66608i		0		−5.13880	+	20.1393i			66.7450i	−46.8501	−	43.6012i	−27.0000				0
151.4	−3.87582	+	0.988963i			5.19615i	14.0439	−	7.66608i		0		−5.13880	−	20.1393i		−	66.7450i	−46.8501	+	43.6012i	−27.0000				0
151.5	−3.04063	−	2.59896i			5.19615i	2.49086	+	15.8049i		0		13.5046	−	15.7996i		−	2.65040i	33.5025	−	54.5305i	−27.0000				0
151.6	−3.04063	+	2.59896i		−	5.19615i	2.49086	−	15.8049i		0		13.5046	+	15.7996i			2.65040i	33.5025	+	54.5305i	−27.0000				0
151.7	−2.03548	−	3.44337i		−	5.19615i	−7.71364	+	14.0178i		0		−17.8923	+	10.5767i			51.0440i	63.9696	−	1.97210i	−27.0000				0
151.8	−2.03548	+	3.44337i			5.19615i	−7.71364	−	14.0178i		0		−17.8923	−	10.5767i		−	51.0440i	63.9696	+	1.97210i	−27.0000				0
151.9	−1.34002	−	3.76887i		−	5.19615i	−12.4087	+	10.1007i		0		−19.5836	+	6.96293i		−	63.7886i	54.6960	+	33.2317i	−27.0000				0
151.10	−1.34002	+	3.76887i			5.19615i	−12.4087	−	10.1007i		0		−19.5836	−	6.96293i			63.7886i	54.6960	−	33.2317i	−27.0000				0
151.11	−0.854601	−	3.90764i			5.19615i	−14.5393	+	6.67895i		0		20.3047	−	4.44064i		−	10.5267i	38.5243	+	51.1066i	−27.0000				0
151.12	−0.854601	+	3.90764i		−	5.19615i	−14.5393	−	6.67895i		0		20.3047	+	4.44064i			10.5267i	38.5243	−	51.1066i	−27.0000				0
151.13	0.854601	−	3.90764i			5.19615i	−14.5393	−	6.67895i		0		20.3047	+	4.44064i		−	10.5267i	−38.5243	+	51.1066i	−27.0000				0
151.14	0.854601	+	3.90764i		−	5.19615i	−14.5393	+	6.67895i		0		20.3047	−	4.44064i			10.5267i	−38.5243	−	51.1066i	−27.0000				0
151.15	1.34002	−	3.76887i		−	5.19615i	−12.4087	−	10.1007i		0		−19.5836	−	6.96293i		−	63.7886i	−54.6960	+	33.2317i	−27.0000				0
151.16	1.34002	+	3.76887i			5.19615i	−12.4087	+	10.1007i		0		−19.5836	+	6.96293i			63.7886i	−54.6960	−	33.2317i	−27.0000				0
151.17	2.03548	−	3.44337i		−	5.19615i	−7.71364	−	14.0178i		0		−17.8923	−	10.5767i			51.0440i	−63.9696	−	1.97210i	−27.0000				0
151.18	2.03548	+	3.44337i			5.19615i	−7.71364	+	14.0178i		0		−17.8923	+	10.5767i		−	51.0440i	−63.9696	+	1.97210i	−27.0000				0
151.19	3.04063	−	2.59896i			5.19615i	2.49086	−	15.8049i		0		13.5046	+	15.7996i		−	2.65040i	−33.5025	−	54.5305i	−27.0000				0
151.20	3.04063	+	2.59896i		−	5.19615i	2.49086	+	15.8049i		0		13.5046	−	15.7996i			2.65040i	−33.5025	+	54.5305i	−27.0000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
20.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	300.5.c.e		24
4.b	odd	2	1	inner	300.5.c.e		24
5.b	even	2	1	inner	300.5.c.e		24
5.c	odd	4	2		60.5.f.a	✓	24
15.e	even	4	2		180.5.f.i		24
20.d	odd	2	1	inner	300.5.c.e		24
20.e	even	4	2		60.5.f.a	✓	24
40.i	odd	4	2		960.5.j.d		24
40.k	even	4	2		960.5.j.d		24
60.l	odd	4	2		180.5.f.i		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
60.5.f.a	✓	24	5.c	odd	4	2
60.5.f.a	✓	24	20.e	even	4	2
180.5.f.i		24	15.e	even	4	2
180.5.f.i		24	60.l	odd	4	2
300.5.c.e		24	1.a	even	1	1	trivial
300.5.c.e		24	4.b	odd	2	1	inner
300.5.c.e		24	5.b	even	2	1	inner
300.5.c.e		24	20.d	odd	2	1	inner
960.5.j.d		24	40.i	odd	4	2
960.5.j.d		24	40.k	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{5}^{\mathrm{new}}(300, [\chi])\):

T7^12 + 15760*T7^10 + 92404320*T7^8 + 239939919616*T7^6 + 240221796962560*T7^4 + 25293558513623040*T7^2 + 165907340518293504

T13^12 - 218544*T13^10 + 18382787808*T13^8 - 747903076611840*T13^6 + 14757459401643948288*T13^4 - 113093462436292330389504*T13^2 + 279951195503529365078016