Newform orbit 29.13.c.a

• Label: 29.13.c.a
• Level: $29$
• Weight: $13$
• Character orbit: 29.c
• Analytic conductor: $26.506$
• Analytic rank: $0$
• Dimension: $58$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(26.5058207010\)
Analytic rank:	\(0\)
Dimension:	\(58\)
Relative dimension:	\(29\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1	−88.1500	−	88.1500i	347.445	+	347.445i			11444.8i			14434.6i		−	61254.6i	−35450.1			647800.	−	647800.i		−	290005.i	1.27241e6	−	1.27241e6i
12.2	−79.7284	−	79.7284i	−520.777	−	520.777i			8617.22i		−	29504.0i			83041.4i	−164320.			360470.	−	360470.i			10976.2i	−2.35231e6	+	2.35231e6i
12.3	−76.2293	−	76.2293i	−132.533	−	132.533i			7525.81i		−	2767.06i			20205.8i	132887.			261452.	−	261452.i		−	496311.i	−210931.	+	210931.i
12.4	−70.5170	−	70.5170i	−767.125	−	767.125i			5849.31i			9904.63i			108191.i	71097.8			123638.	−	123638.i			645520.i	698445.	−	698445.i
12.5	−69.9680	−	69.9680i	814.355	+	814.355i			5695.05i		−	19209.4i		−	113958.i	−6147.85			111882.	−	111882.i			794908.i	−1.34405e6	+	1.34405e6i
12.6	−58.0743	−	58.0743i	433.237	+	433.237i			2649.26i			10278.3i		−	50319.9i	−72219.2			−84018.7	+	84018.7i		−	156053.i	596905.	−	596905.i
12.7	−54.5113	−	54.5113i	−434.460	−	434.460i			1846.95i			19548.9i			47365.9i	−201373.			−122598.	+	122598.i		−	153930.i	1.06564e6	−	1.06564e6i
12.8	−44.8874	−	44.8874i	80.4158	+	80.4158i		−	66.2505i		−	12643.6i		−	7219.30i	209784.			−186832.	+	186832.i		−	518508.i	−567536.	+	567536.i
12.9	−44.4183	−	44.4183i	834.913	+	834.913i		−	150.028i			28014.5i		−	74170.9i	122123.			−188601.	+	188601.i			862719.i	1.24436e6	−	1.24436e6i
12.10	−33.9863	−	33.9863i	−37.2586	−	37.2586i		−	1785.87i		−	14007.5i			2532.56i	−78700.5			−199903.	+	199903.i		−	528665.i	−476064.	+	476064.i
12.11	−29.6845	−	29.6845i	−878.412	−	878.412i		−	2333.66i		−	15619.8i			52150.4i	10196.8			−190861.	+	190861.i			1.01178e6i	−463667.	+	463667.i
12.12	−15.4217	−	15.4217i	−236.320	−	236.320i		−	3620.34i			24342.5i			7288.92i	119306.			−118999.	+	118999.i		−	419746.i	375403.	−	375403.i
12.13	−12.2710	−	12.2710i	762.089	+	762.089i		−	3794.84i		−	6703.86i		−	18703.2i	−134602.			−96828.8	+	96828.8i			630118.i	−82263.3	+	82263.3i
12.14	−9.03178	−	9.03178i	−704.167	−	704.167i		−	3932.85i			8770.94i			12719.8i	37099.6			−72514.8	+	72514.8i			460261.i	79217.2	−	79217.2i
12.15	2.50807	+	2.50807i	773.536	+	773.536i		−	4083.42i		−	10269.1i			3880.17i	192386.			20514.6	−	20514.6i			665275.i	25755.5	−	25755.5i
12.16	8.76721	+	8.76721i	327.395	+	327.395i		−	3942.27i			12032.8i			5740.68i	−63314.5			70473.2	−	70473.2i		−	317066.i	−105494.	+	105494.i
12.17	18.1237	+	18.1237i	−105.386	−	105.386i		−	3439.06i		−	24861.6i		−	3819.95i	4681.32			136563.	−	136563.i		−	509229.i	450583.	−	450583.i
12.18	26.4284	+	26.4284i	−670.941	−	670.941i		−	2699.08i			5810.81i		−	35463.8i	−231201.			179583.	−	179583.i			368882.i	−153570.	+	153570.i
12.19	33.1274	+	33.1274i	−631.679	−	631.679i		−	1901.16i		−	13469.1i		−	41851.7i	113718.			198670.	−	198670.i			266596.i	446197.	−	446197.i
12.20	43.6471	+	43.6471i	−94.5951	−	94.5951i		−	285.862i			15326.9i		−	8257.61i	49832.3			191256.	−	191256.i		−	513545.i	−668974.	+	668974.i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	29.13.c.a	✓	58
29.c	odd	4	1	inner	29.13.c.a	✓	58

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
29.13.c.a	✓	58	1.a	even	1	1	trivial
29.13.c.a	✓	58	29.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{13}^{\mathrm{new}}(29, [\chi])\).