Newform orbit 23.15.d.a

• Label: 23.15.d.a
• Level: $23$
• Weight: $15$
• Character orbit: 23.d
• Analytic conductor: $28.596$
• Analytic rank: $0$
• Dimension: $270$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.5956626749\)
Analytic rank:	\(0\)
Dimension:	\(270\)
Relative dimension:	\(27\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 270 q + 173 q^{2} + 2149 q^{3} - 184115 q^{4} - 11 q^{5} + 44722 q^{6} - 11 q^{7} + 7241658 q^{8} - 39199166 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−239.810	−	70.4144i	1474.41	−	1701.56i	38767.3	+	24914.3i	40294.5	+	5793.47i	−473392.	+	304231.i	341082.	−	155767.i	−4.86086e6	−	5.60973e6i	−40735.0	−	283318.i	−9.25506e6	−	4.22664e6i
5.2	−215.886	−	63.3897i	−2125.96	+	2453.49i	28805.2	+	18512.0i	7903.43	+	1136.34i	614491.	−	394909.i	96970.1	−	44284.8i	−2.63109e6	−	3.03644e6i	−819216.	−	5.69777e6i	−1.63420e6	−	746316.i
5.3	−192.648	−	56.5664i	−516.411	+	595.970i	20130.2	+	12936.9i	−96544.3	−	13881.0i	133197.	−	85600.6i	133595.	−	61010.7i	−992020.	−	1.14485e6i	592187.	+	4.11875e6i	1.78138e7	+	8.13530e6i
5.4	−182.537	−	53.5978i	43.2855	−	49.9541i	16664.0	+	10709.3i	88332.7	+	12700.3i	−10578.6	+	6798.48i	−1.44754e6	+	661071.i	−426644.	−	492373.i	680066.	+	4.72996e6i	−1.54433e7	−	7.05272e6i
5.5	−174.358	−	51.1962i	2314.56	−	2671.14i	13996.7	+	8995.12i	−126019.	−	18118.8i	−540315.	+	347240.i	−496327.	+	226665.i	−30212.8	−	34867.4i	−1.09714e6	−	7.63076e6i	2.10449e7	+	9.61087e6i
5.6	−162.162	−	47.6150i	1111.61	−	1282.87i	10246.1	+	6584.79i	32770.0	+	4711.62i	−241345.	+	155103.i	862654.	−	393961.i	465328.	+	537017.i	270616.	+	1.88217e6i	−5.08970e6	−	2.32439e6i
5.7	−125.080	−	36.7268i	−1316.56	+	1519.39i	513.046	+	329.714i	138756.	+	19950.1i	220477.	−	141692.i	793580.	−	362416.i	1.34661e6	+	1.55407e6i	105471.	+	733564.i	−1.66229e7	−	7.59143e6i
5.8	−102.168	−	29.9991i	2406.75	−	2777.53i	−4244.84	−	2727.99i	72015.7	+	10354.3i	−329215.	+	211573.i	−51794.5	+	23653.7i	1.49430e6	+	1.72452e6i	−1.24157e6	−	8.63534e6i	−7.04705e6	−	3.21828e6i
5.9	−101.219	−	29.7205i	−1577.18	+	1820.17i	−4421.18	−	2841.32i	−68025.4	−	9780.58i	213737.	−	137360.i	169076.	−	77214.4i	1.49491e6	+	1.72522e6i	−144812.	−	1.00719e6i	6.59476e6	+	3.01173e6i
5.10	−76.7679	−	22.5411i	184.251	−	212.637i	−8397.89	−	5397.00i	−65621.6	−	9434.97i	−18937.6	+	12170.5i	−1.11550e6	+	509430.i	1.38147e6	+	1.59430e6i	669421.	+	4.65593e6i	4.82496e6	+	2.20349e6i
5.11	−72.6742	−	21.3391i	−2557.19	+	2951.16i	−8956.91	−	5756.26i	−5706.48	−	820.468i	248817.	−	159905.i	−701947.	+	320568.i	1.34076e6	+	1.54732e6i	−1.48941e6	−	1.03591e7i	397206.	+	181398.i
5.12	−53.9715	−	15.8475i	306.188	−	353.360i	−11121.3	−	7147.24i	−52369.4	−	7529.58i	−22125.3	+	14219.1i	1.12010e6	−	511532.i	1.09049e6	+	1.25849e6i	649575.	+	4.51790e6i	2.70713e6	+	1.23630e6i
5.13	−18.9656	−	5.56881i	1300.36	−	1500.69i	−13454.4	−	8646.63i	40364.7	+	5803.57i	−33019.1	+	21220.1i	−455018.	+	207800.i	419097.	+	483664.i	119540.	+	831420.i	−733223.	−	334852.i
5.14	22.9608	+	6.74191i	−1346.51	+	1553.96i	−13301.4	−	8548.26i	81926.2	+	11779.2i	−41393.6	+	26602.1i	−122133.	+	55776.2i	−504531.	−	582260.i	78999.3	+	549452.i	1.80168e6	+	822799.i
5.15	41.2203	+	12.1034i	2006.50	−	2315.62i	−12230.5	−	7860.05i	−102785.	−	14778.2i	110735.	−	71165.2i	373207.	−	170438.i	−869944.	−	1.00397e6i	−655385.	−	4.55830e6i	−4.05795e6	−	1.85320e6i
5.16	52.3513	+	15.3717i	−198.734	+	229.351i	−11278.7	−	7248.40i	76643.7	+	11019.7i	−13929.5	+	8951.94i	−297141.	+	135700.i	−1.06444e6	−	1.22843e6i	667581.	+	4.64313e6i	3.84301e6	+	1.75504e6i
5.17	67.1845	+	19.7271i	−2168.41	+	2502.47i	−9658.50	−	6207.14i	−59403.5	−	8540.93i	−195050.	+	125351.i	1.32939e6	−	607114.i	−1.27772e6	−	1.47457e6i	−879702.	−	6.11846e6i	−3.82250e6	−	1.74568e6i
5.18	77.1586	+	22.6558i	−1079.39	+	1245.68i	−8342.93	−	5361.68i	−146358.	−	21043.0i	−111506.	+	71660.5i	−868722.	+	396732.i	−1.38506e6	−	1.59844e6i	294047.	+	2.04514e6i	−1.08160e7	−	4.93950e6i
5.19	110.343	+	32.3998i	1950.82	−	2251.36i	−2657.17	−	1707.66i	132314.	+	19023.9i	288204.	−	185217.i	1.09279e6	−	499061.i	−1.47176e6	−	1.69850e6i	−582262.	−	4.04972e6i	1.39836e7	+	6.38610e6i
5.20	133.250	+	39.1257i	2339.92	−	2700.41i	2441.62	+	1569.14i	9176.41	+	1319.37i	417450.	−	268279.i	−1.39751e6	+	638220.i	−1.22607e6	−	1.41496e6i	−1.13631e6	−	7.90321e6i	1.17113e6	+	534839.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.d	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.15.d.a	✓	270
23.d	odd	22	1	inner	23.15.d.a	✓	270

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.15.d.a	✓	270	1.a	even	1	1	trivial
23.15.d.a	✓	270	23.d	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{15}^{\mathrm{new}}(23, [\chi])\).