Newform orbit 12.14.b.a

• Label: 12.14.b.a
• Level: $12$
• Weight: $14$
• Character orbit: 12.b
• Analytic conductor: $12.868$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.8677114742\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−89.8019	−	11.2966i	−433.314	+	1185.99i	7936.77	+	2028.92i		−	24994.7i	52310.1	−	101609.i		−	71320.8i	−689818.	−	271859.i	−1.21880e6	−	1.02781e6i	−282356.	+	2.24457e6i
11.2	−89.8019	+	11.2966i	−433.314	−	1185.99i	7936.77	−	2028.92i			24994.7i	52310.1	+	101609.i			71320.8i	−689818.	+	271859.i	−1.21880e6	+	1.02781e6i	−282356.	−	2.24457e6i
11.3	−83.2487	−	35.5199i	1204.82	+	377.813i	5668.68	+	5913.96i			53567.1i	−86879.4	−	74247.3i		−	133564.i	−261847.	−	693680.i	1.30884e6	+	910390.i	1.90270e6	−	4.45939e6i
11.4	−83.2487	+	35.5199i	1204.82	−	377.813i	5668.68	−	5913.96i		−	53567.1i	−86879.4	+	74247.3i			133564.i	−261847.	+	693680.i	1.30884e6	−	910390.i	1.90270e6	+	4.45939e6i
11.5	−63.1407	−	64.8479i	−1256.10	−	128.555i	−218.513	+	8189.09i			1788.84i	70974.7	+	89572.8i			316886.i	544842.	−	502894.i	1.56127e6	+	322956.i	116003.	−	112949.i
11.6	−63.1407	+	64.8479i	−1256.10	+	128.555i	−218.513	−	8189.09i		−	1788.84i	70974.7	−	89572.8i		−	316886.i	544842.	+	502894.i	1.56127e6	−	322956.i	116003.	+	112949.i
11.7	−61.4564	−	66.4463i	544.543	−	1139.21i	−638.220	+	8167.10i		−	30890.7i	−109162.	+	33828.8i		−	363071.i	581896.	−	459513.i	−1.00127e6	−	1.24070e6i	−2.05257e6	+	1.89843e6i
11.8	−61.4564	+	66.4463i	544.543	+	1139.21i	−638.220	−	8167.10i			30890.7i	−109162.	−	33828.8i			363071.i	581896.	+	459513.i	−1.00127e6	+	1.24070e6i	−2.05257e6	−	1.89843e6i
11.9	−26.1905	−	86.6375i	919.540	+	865.314i	−6820.12	+	4538.16i		−	34796.6i	50885.4	−	102330.i			298175.i	571797.	+	472022.i	96786.4	+	1.59138e6i	−3.01469e6	+	911338.i
11.10	−26.1905	+	86.6375i	919.540	−	865.314i	−6820.12	−	4538.16i			34796.6i	50885.4	+	102330.i		−	298175.i	571797.	−	472022.i	96786.4	−	1.59138e6i	−3.01469e6	−	911338.i
11.11	−9.20327	−	90.0405i	−618.744	+	1100.67i	−8022.60	+	1657.33i			49220.1i	104800.	+	45582.3i		−	527913.i	223061.	+	707106.i	−828634.	−	1.36207e6i	4.43181e6	−	452986.i
11.12	−9.20327	+	90.0405i	−618.744	−	1100.67i	−8022.60	−	1657.33i		−	49220.1i	104800.	−	45582.3i			527913.i	223061.	−	707106.i	−828634.	+	1.36207e6i	4.43181e6	+	452986.i
11.13	9.20327	−	90.0405i	618.744	−	1100.67i	−8022.60	−	1657.33i			49220.1i	−93410.6	−	65841.9i			527913.i	−223061.	+	707106.i	−828634.	−	1.36207e6i	4.43181e6	+	452986.i
11.14	9.20327	+	90.0405i	618.744	+	1100.67i	−8022.60	+	1657.33i		−	49220.1i	−93410.6	+	65841.9i		−	527913.i	−223061.	−	707106.i	−828634.	+	1.36207e6i	4.43181e6	−	452986.i
11.15	26.1905	−	86.6375i	−919.540	−	865.314i	−6820.12	−	4538.16i		−	34796.6i	−99051.9	+	57003.7i		−	298175.i	−571797.	+	472022.i	96786.4	+	1.59138e6i	−3.01469e6	−	911338.i
11.16	26.1905	+	86.6375i	−919.540	+	865.314i	−6820.12	+	4538.16i			34796.6i	−99051.9	−	57003.7i			298175.i	−571797.	−	472022.i	96786.4	−	1.59138e6i	−3.01469e6	+	911338.i
11.17	61.4564	−	66.4463i	−544.543	+	1139.21i	−638.220	−	8167.10i		−	30890.7i	42230.6	+	106195.i			363071.i	−581896.	−	459513.i	−1.00127e6	−	1.24070e6i	−2.05257e6	−	1.89843e6i
11.18	61.4564	+	66.4463i	−544.543	−	1139.21i	−638.220	+	8167.10i			30890.7i	42230.6	−	106195.i		−	363071.i	−581896.	+	459513.i	−1.00127e6	+	1.24070e6i	−2.05257e6	+	1.89843e6i
11.19	63.1407	−	64.8479i	1256.10	+	128.555i	−218.513	−	8189.09i			1788.84i	87647.7	−	73338.7i		−	316886.i	−544842.	−	502894.i	1.56127e6	+	322956.i	116003.	+	112949.i
11.20	63.1407	+	64.8479i	1256.10	−	128.555i	−218.513	+	8189.09i		−	1788.84i	87647.7	+	73338.7i			316886.i	−544842.	+	502894.i	1.56127e6	−	322956.i	116003.	−	112949.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	12.14.b.a	✓	24
3.b	odd	2	1	inner	12.14.b.a	✓	24
4.b	odd	2	1	inner	12.14.b.a	✓	24
12.b	even	2	1	inner	12.14.b.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
12.14.b.a	✓	24	1.a	even	1	1	trivial
12.14.b.a	✓	24	3.b	odd	2	1	inner
12.14.b.a	✓	24	4.b	odd	2	1	inner
12.14.b.a	✓	24	12.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(12, [\chi])\).