Newform orbit 3234.2.e.d

• Label: 3234.2.e.d
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.e
• Analytic conductor: $25.824$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(25.8236200137\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2155.1		−	1.00000i			1.00000i	−1.00000				−	4.05345i	1.00000				0				1.00000i	−1.00000			−4.05345
2155.2		−	1.00000i			1.00000i	−1.00000				−	3.45711i	1.00000				0				1.00000i	−1.00000			−3.45711
2155.3		−	1.00000i			1.00000i	−1.00000				−	2.66749i	1.00000				0				1.00000i	−1.00000			−2.66749
2155.4		−	1.00000i			1.00000i	−1.00000				−	0.516505i	1.00000				0				1.00000i	−1.00000			−0.516505
2155.5		−	1.00000i			1.00000i	−1.00000				−	0.357203i	1.00000				0				1.00000i	−1.00000			−0.357203
2155.6		−	1.00000i			1.00000i	−1.00000				−	0.313884i	1.00000				0				1.00000i	−1.00000			−0.313884
2155.7		−	1.00000i			1.00000i	−1.00000					0.500309i	1.00000				0				1.00000i	−1.00000			0.500309
2155.8		−	1.00000i			1.00000i	−1.00000					0.942563i	1.00000				0				1.00000i	−1.00000			0.942563
2155.9		−	1.00000i			1.00000i	−1.00000					1.58222i	1.00000				0				1.00000i	−1.00000			1.58222
2155.10		−	1.00000i			1.00000i	−1.00000					1.98215i	1.00000				0				1.00000i	−1.00000			1.98215
2155.11		−	1.00000i			1.00000i	−1.00000					2.84462i	1.00000				0				1.00000i	−1.00000			2.84462
2155.12		−	1.00000i			1.00000i	−1.00000					3.51377i	1.00000				0				1.00000i	−1.00000			3.51377
2155.13			1.00000i		−	1.00000i	−1.00000				−	3.51377i	1.00000				0			−	1.00000i	−1.00000			3.51377
2155.14			1.00000i		−	1.00000i	−1.00000				−	2.84462i	1.00000				0			−	1.00000i	−1.00000			2.84462
2155.15			1.00000i		−	1.00000i	−1.00000				−	1.98215i	1.00000				0			−	1.00000i	−1.00000			1.98215
2155.16			1.00000i		−	1.00000i	−1.00000				−	1.58222i	1.00000				0			−	1.00000i	−1.00000			1.58222
2155.17			1.00000i		−	1.00000i	−1.00000				−	0.942563i	1.00000				0			−	1.00000i	−1.00000			0.942563
2155.18			1.00000i		−	1.00000i	−1.00000				−	0.500309i	1.00000				0			−	1.00000i	−1.00000			0.500309
2155.19			1.00000i		−	1.00000i	−1.00000					0.313884i	1.00000				0			−	1.00000i	−1.00000			−0.313884
2155.20			1.00000i		−	1.00000i	−1.00000					0.357203i	1.00000				0			−	1.00000i	−1.00000			−0.357203

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
77.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3234.2.e.d	yes	24
7.b	odd	2	1		3234.2.e.c	✓	24
11.b	odd	2	1		3234.2.e.c	✓	24
77.b	even	2	1	inner	3234.2.e.d	yes	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3234.2.e.c	✓	24	7.b	odd	2	1
3234.2.e.c	✓	24	11.b	odd	2	1
3234.2.e.d	yes	24	1.a	even	1	1	trivial
3234.2.e.d	yes	24	77.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3234, [\chi])\):

T5^24 + 64*T5^22 + 1696*T5^20 + 24160*T5^18 + 201024*T5^16 + 995200*T5^14 + 2870592*T5^12 + 4574208*T5^10 + 3727360*T5^8 + 1498112*T5^6 + 301056*T5^4 + 28672*T5^2 + 1024

\( T_{13}^{12} - 76 T_{13}^{10} - 48 T_{13}^{9} + 2134 T_{13}^{8} + 2432 T_{13}^{7} - 26512 T_{13}^{6} - 40000 T_{13}^{5} + 138220 T_{13}^{4} + 247808 T_{13}^{3} - 211312 T_{13}^{2} - 510912 T_{13} - 207224 \)