Newform orbit 23.14.c.a

• Label: 23.14.c.a
• Level: $23$
• Weight: $14$
• Character orbit: 23.c
• Analytic conductor: $24.663$
• Analytic rank: $0$
• Dimension: $250$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.6631136589\)
Analytic rank:	\(0\)
Dimension:	\(250\)
Relative dimension:	\(25\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 250 q - 11 q^{2} - 1207 q^{3} - 114699 q^{4} - 41875 q^{5} - 125668 q^{6} + 240331 q^{7} + 562996 q^{8} - 13202058 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−148.558	−	95.4721i	40.5498	+	282.030i	9551.33	+	20914.5i	−21008.0	−	6168.50i	20902.0	−	45769.1i	62672.2	−	72327.6i	371952.	−	2.58699e6i	1.45184e6	−	426300.i	2.53197e6	+	2.92205e6i
2.2	−124.099	−	79.7538i	186.867	+	1299.69i	5636.91	+	12343.1i	49603.5	+	14564.9i	80464.9	−	176193.i	166766.	−	192458.i	112891.	−	785176.i	−124521.	+	36562.6i	−4.99415e6	−	5.76356e6i
2.3	−120.926	−	77.7141i	−171.197	−	1190.70i	5180.43	+	11343.6i	19775.0	+	5806.45i	−71832.2	+	157291.i	−244189.	+	281809.i	87524.8	−	608749.i	141282.	−	41484.3i	−1.94006e6	−	2.23894e6i
2.4	−117.776	−	75.6898i	−286.016	−	1989.28i	4739.08	+	10377.1i	−53672.4	−	15759.6i	−116883.	+	255938.i	219501.	−	253317.i	64077.1	−	445666.i	−2.34571e6	+	688762.i	5.12846e6	+	5.91856e6i
2.5	−110.511	−	71.0210i	309.935	+	2155.64i	3765.58	+	8245.46i	−12665.7	−	3718.98i	118845.	−	260234.i	−372845.	+	430286.i	16313.7	−	113464.i	−3.02100e6	+	887044.i	1.13557e6	+	1.31052e6i
2.6	−90.8053	−	58.3570i	−216.759	−	1507.59i	1436.98	+	3146.55i	40599.2	+	11921.0i	−68295.8	+	149547.i	272495.	−	314476.i	−72703.8	+	505666.i	−696111.	+	204397.i	−2.99095e6	−	3.45174e6i
2.7	−89.9076	−	57.7801i	138.271	+	961.699i	1341.76	+	2938.04i	−33082.3	−	9713.85i	43135.4	−	94453.5i	113673.	−	131185.i	−75471.5	+	524916.i	623995.	−	183221.i	2.41309e6	+	2.78485e6i
2.8	−52.7445	−	33.8968i	−17.4363	−	121.272i	−1770.09	−	3875.97i	8956.10	+	2629.75i	−3191.06	+	6987.45i	66066.1	−	76244.3i	−111116.	+	772826.i	1.51534e6	−	444944.i	−383244.	−	442288.i
2.9	−47.8703	−	30.7644i	−115.399	−	802.615i	−2057.96	−	4506.31i	−46665.6	−	13702.2i	−19167.8	+	41971.6i	−280171.	+	323334.i	−106459.	+	740439.i	898868.	−	263931.i	1.81235e6	+	2.09157e6i
2.10	−36.9863	−	23.7697i	130.350	+	906.604i	−2600.09	−	5693.40i	60299.7	+	17705.6i	16728.5	−	36630.3i	−302922.	+	349590.i	−90419.7	+	628883.i	724802.	−	212821.i	−1.80941e6	−	2.08817e6i
2.11	−30.2619	−	19.4481i	339.134	+	2358.73i	−2865.53	−	6274.63i	20394.1	+	5988.26i	35610.0	−	77975.1i	306140.	−	353305.i	−77251.7	+	537297.i	−3.91885e6	+	1.15068e6i	−500704.	−	577843.i
2.12	−18.4132	−	11.8335i	−342.090	−	2379.29i	−3204.06	−	7015.92i	4985.34	+	1463.83i	−21856.2	+	47858.4i	−109186.	+	126007.i	−49543.2	+	344581.i	−4.01424e6	+	1.17869e6i	−74474.0	−	85947.5i
2.13	7.11848	+	4.57477i	−142.657	−	992.199i	−3373.34	−	7386.57i	11654.7	+	3422.12i	3523.58	−	7715.57i	174823.	−	201756.i	19643.9	−	136627.i	565634.	−	166085.i	67308.1	+	77677.7i
2.14	16.7435	+	10.7604i	151.836	+	1056.05i	−3238.52	−	7091.37i	7999.99	+	2349.01i	−8821.17	+	19315.7i	−26234.2	+	30275.8i	45285.5	−	314968.i	437563.	−	128480.i	108671.	+	125413.i
2.15	17.0328	+	10.9463i	262.763	+	1827.56i	−3232.78	−	7078.81i	−52729.4	−	15482.7i	−15529.5	+	34004.8i	−49738.1	+	57400.9i	46028.4	−	320134.i	−1.74119e6	+	511260.i	−728651.	−	840908.i
2.16	34.5392	+	22.1970i	−142.765	−	992.953i	−2702.83	−	5918.37i	−61204.1	−	17971.1i	17109.6	−	37464.8i	340877.	−	393393.i	85882.3	−	597325.i	564167.	−	165655.i	−1.71503e6	−	1.97926e6i
2.17	63.3663	+	40.7231i	−166.481	−	1157.90i	−1046.16	−	2290.76i	65468.7	+	19223.3i	36604.0	−	80151.5i	−13228.2	+	15266.2i	114811.	−	798531.i	216723.	−	63635.6i	3.36568e6	+	3.88420e6i
2.18	65.2031	+	41.9035i	117.297	+	815.821i	−907.541	−	1987.24i	−8464.88	−	2485.51i	−26537.6	+	58109.2i	−218656.	+	252343.i	114459.	−	796078.i	877936.	−	257785.i	−447785.	−	516771.i
2.19	75.6052	+	48.5885i	−205.966	−	1432.52i	−47.7759	−	104.615i	−13424.6	−	3941.83i	54032.1	−	118314.i	−263256.	+	303813.i	106248.	−	738969.i	−479963.	+	140930.i	−823445.	−	950307.i
2.20	90.4844	+	58.1508i	126.551	+	880.179i	1402.84	+	3071.78i	21223.6	+	6231.81i	−39732.3	+	87001.5i	348892.	−	402643.i	73705.1	−	512630.i	771042.	−	226398.i	1.55802e6	+	1.79805e6i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.14.c.a	✓	250
23.c	even	11	1	inner	23.14.c.a	✓	250

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.14.c.a	✓	250	1.a	even	1	1	trivial
23.14.c.a	✓	250	23.c	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(23, [\chi])\).