Newform orbit 1860.2.o.a

• Label: 1860.2.o.a
• Level: $1860$
• Weight: $2$
• Character orbit: 1860.o
• Analytic conductor: $14.852$
• Analytic rank: $0$
• Dimension: $44$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.o (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.8521747760\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 8 q^{7} - 8 q^{19} - 44 q^{25} - 28 q^{33} + 4 q^{39} - 4 q^{45} + 60 q^{49} + 8 q^{51} + 20 q^{63} - 56 q^{67} + 28 q^{69} + 60 q^{81} - 44 q^{87} + 4 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1301.1		0		−1.71659	−	0.230889i		0			−	1.00000i		0		2.24276				0		2.89338	+	0.792685i		0
1301.2		0		−1.71659	+	0.230889i		0				1.00000i		0		2.24276				0		2.89338	−	0.792685i		0
1301.3		0		−1.68193	−	0.413652i		0			−	1.00000i		0		−3.06485				0		2.65778	+	1.39147i		0
1301.4		0		−1.68193	+	0.413652i		0				1.00000i		0		−3.06485				0		2.65778	−	1.39147i		0
1301.5		0		−1.67660	−	0.434770i		0				1.00000i		0		−2.24883				0		2.62195	+	1.45787i		0
1301.6		0		−1.67660	+	0.434770i		0			−	1.00000i		0		−2.24883				0		2.62195	−	1.45787i		0
1301.7		0		−1.64097	−	0.554285i		0			−	1.00000i		0		4.08046				0		2.38554	+	1.81912i		0
1301.8		0		−1.64097	+	0.554285i		0				1.00000i		0		4.08046				0		2.38554	−	1.81912i		0
1301.9		0		−1.38957	−	1.03397i		0				1.00000i		0		3.47810				0		0.861798	+	2.87355i		0
1301.10		0		−1.38957	+	1.03397i		0			−	1.00000i		0		3.47810				0		0.861798	−	2.87355i		0
1301.11		0		−1.17920	−	1.26865i		0				1.00000i		0		−1.14123				0		−0.218954	+	2.99200i		0
1301.12		0		−1.17920	+	1.26865i		0			−	1.00000i		0		−1.14123				0		−0.218954	−	2.99200i		0
1301.13		0		−1.05953	−	1.37018i		0			−	1.00000i		0		−0.393828				0		−0.754810	+	2.90349i		0
1301.14		0		−1.05953	+	1.37018i		0				1.00000i		0		−0.393828				0		−0.754810	−	2.90349i		0
1301.15		0		−0.592574	−	1.62753i		0				1.00000i		0		−5.03827				0		−2.29771	+	1.92886i		0
1301.16		0		−0.592574	+	1.62753i		0			−	1.00000i		0		−5.03827				0		−2.29771	−	1.92886i		0
1301.17		0		−0.575778	−	1.63355i		0			−	1.00000i		0		−0.333170				0		−2.33696	+	1.88112i		0
1301.18		0		−0.575778	+	1.63355i		0				1.00000i		0		−0.333170				0		−2.33696	−	1.88112i		0
1301.19		0		−0.280887	−	1.70912i		0				1.00000i		0		0.331083				0		−2.84220	+	0.960142i		0
1301.20		0		−0.280887	+	1.70912i		0			−	1.00000i		0		0.331083				0		−2.84220	−	0.960142i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
31.b	odd	2	1	inner
93.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1860.2.o.a	✓	44
3.b	odd	2	1	inner	1860.2.o.a	✓	44
31.b	odd	2	1	inner	1860.2.o.a	✓	44
93.c	even	2	1	inner	1860.2.o.a	✓	44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1860.2.o.a	✓	44	1.a	even	1	1	trivial
1860.2.o.a	✓	44	3.b	odd	2	1	inner
1860.2.o.a	✓	44	31.b	odd	2	1	inner
1860.2.o.a	✓	44	93.c	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1860, [\chi])\).