Newform orbit 1904.4.a.b

• Label: 1904.4.a.b
• Level: $1904$
• Weight: $4$
• Character orbit: 1904.a
• Self dual: yes
• Analytic conductor: $112.340$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1904.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(112.339636651\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{93}) \)
Defining polynomial:	\( x^{2} - x - 23 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{93})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (-b + 3) * q^3 + (b + 4) * q^5 + 7 * q^7 + (-5*b + 5) * q^9 + (8*b - 2) * q^11 + (-8*b - 10) * q^13 + (-2*b - 11) * q^15 + 17 * q^17 + (4*b - 8) * q^19 + (-7*b + 21) * q^21 + (2*b - 26) * q^23 + (9*b - 86) * q^25 + (12*b + 49) * q^27 + (28*b - 118) * q^29 + (27*b - 108) * q^31 + (18*b - 190) * q^33 + (7*b + 28) * q^35 + (32*b - 176) * q^37 + (-6*b + 154) * q^39 + (-7*b - 225) * q^41 + (-69*b + 69) * q^43 + (-20*b - 95) * q^45 + (-6*b + 390) * q^47 + 49 * q^49 + (-17*b + 51) * q^51 + (-15*b - 358) * q^53 + (38*b + 176) * q^55 + (16*b - 116) * q^57 - 148 * q^59 + (-69*b - 135) * q^61 + (-35*b + 35) * q^63 + (-50*b - 224) * q^65 + (49*b - 258) * q^67 + (30*b - 124) * q^69 + (-16*b - 100) * q^71 + (-21*b + 421) * q^73 + (104*b - 465) * q^75 + (56*b - 14) * q^77 + (78*b - 54) * q^79 + (110*b - 264) * q^81 + (-158*b + 258) * q^83 + (17*b + 68) * q^85 + (174*b - 998) * q^87 + (38*b - 478) * q^89 + (-56*b - 70) * q^91 + (162*b - 945) * q^93 + (12*b + 60) * q^95 + (109*b - 512) * q^97 + (10*b - 930) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 5 * q^3 + 9 * q^5 + 14 * q^7 + 5 * q^9 + 4 * q^11 - 28 * q^13 - 24 * q^15 + 34 * q^17 - 12 * q^19 + 35 * q^21 - 50 * q^23 - 163 * q^25 + 110 * q^27 - 208 * q^29 - 189 * q^31 - 362 * q^33 + 63 * q^35 - 320 * q^37 + 302 * q^39 - 457 * q^41 + 69 * q^43 - 210 * q^45 + 774 * q^47 + 98 * q^49 + 85 * q^51 - 731 * q^53 + 390 * q^55 - 216 * q^57 - 296 * q^59 - 339 * q^61 + 35 * q^63 - 498 * q^65 - 467 * q^67 - 218 * q^69 - 216 * q^71 + 821 * q^73 - 826 * q^75 + 28 * q^77 - 30 * q^79 - 418 * q^81 + 358 * q^83 + 153 * q^85 - 1822 * q^87 - 918 * q^89 - 196 * q^91 - 1728 * q^93 + 132 * q^95 - 915 * q^97 - 1850 * q^99

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

5.32183
−4.32183

0

−2.32183

0

9.32183

0

7.00000

0

−21.6091

0

1.2

0

7.32183

0

−0.321825

0

7.00000

0

26.6091

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(7\)	\( -1 \)
\(17\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1904.4.a.b		2
4.b	odd	2	1		238.4.a.a	✓	2
12.b	even	2	1		2142.4.a.l		2
28.d	even	2	1		1666.4.a.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
238.4.a.a	✓	2	4.b	odd	2	1
1666.4.a.c		2	28.d	even	2	1
1904.4.a.b		2	1.a	even	1	1	trivial
2142.4.a.l		2	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} - 5T_{3} - 17 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1904))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 5T - 17 \)
$5$	\( T^{2} - 9T - 3 \)
$7$	\( (T - 7)^{2} \)
$11$	\( T^{2} - 4T - 1484 \)