Newform orbit 4015.2.a.c

• Label: 4015.2.a.c
• Level: $4015$
• Weight: $2$
• Character orbit: 4015.a
• Self dual: yes
• Analytic conductor: $32.060$
• Analytic rank: $1$
• Dimension: $23$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(32.0599364115\)
Analytic rank:	\(1\)
Dimension:	\(23\)
Twist minimal:	yes
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.63381			−0.811587			4.93698			1.00000			2.13757			5.26915			−7.73545			−2.34133			−2.63381
1.2	−2.41301			1.23805			3.82260			1.00000			−2.98742			−1.94006			−4.39795			−1.46724			−2.41301
1.3	−2.26107			−2.17834			3.11244			1.00000			4.92537			1.01936			−2.51531			1.74515			−2.26107
1.4	−2.15888			1.54599			2.66074			1.00000			−3.33759			2.48210			−1.42646			−0.609922			−2.15888
1.5	−2.00725			−2.63655			2.02904			1.00000			5.29220			−1.13661			−0.0582891			3.95138			−2.00725
1.6	−1.63550			2.32797			0.674867			1.00000			−3.80740			−0.601850			2.16726			2.41945			−1.63550
1.7	−1.22952			−0.451066			−0.488282			1.00000			0.554594			−2.48868			3.05939			−2.79654			−1.22952
1.8	−1.17870			−1.42513			−0.610675			1.00000			1.67979			3.29739			3.07719			−0.969018			−1.17870
1.9	−0.975417			1.70884			−1.04856			1.00000			−1.66683			0.984932			2.97362			−0.0798559			−0.975417
1.10	−0.760826			0.764917			−1.42114			1.00000			−0.581969			−2.66383			2.60290			−2.41490			−0.760826
1.11	−0.692372			−2.63531			−1.52062			1.00000			1.82461			0.337135			2.43758			3.94484			−0.692372
1.12	−0.197331			2.44280			−1.96106			1.00000			−0.482041			−1.78119			0.781640			2.96728			−0.197331
1.13	0.418197			2.15176			−1.82511			1.00000			0.899862			0.524806			−1.59965			1.63009			0.418197
1.14	0.422103			−2.19245			−1.82183			1.00000			−0.925438			−3.51396			−1.61321			1.80682			0.422103
1.15	0.615983			−0.785692			−1.62056			1.00000			−0.483973			2.63763			−2.23021			−2.38269			0.615983
1.16	0.661798			−2.32231			−1.56202			1.00000			−1.53690			−0.917277			−2.35734			2.39311			0.661798
1.17	1.20516			1.14152			−0.547593			1.00000			1.37572			3.42329			−3.07025			−1.69692			1.20516
1.18	1.30572			1.83317			−0.295101			1.00000			2.39360			−4.41824			−2.99675			0.360505			1.30572
1.19	1.83759			−0.530531			1.37674			1.00000			−0.974898			1.03293			−1.14530			−2.71854			1.83759
1.20	1.92108			−3.32354			1.69056			1.00000			−6.38479			2.35268			−0.594467			8.04590			1.92108

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(-1\)
\(11\)	\(1\)
\(73\)	\(-1\)

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	4015.2.a.c	✓	23

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4015.2.a.c	✓	23	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^23 + 3*T2^22 - 26*T2^21 - 81*T2^20 + 281*T2^19 + 922*T2^18 - 1638*T2^17 - 5787*T2^16 + 5566*T2^15 + 21981*T2^14 - 11040*T2^13 - 52227*T2^12 + 11857*T2^11 + 77754*T2^10 - 5190*T2^9 - 71124*T2^8 - 702*T2^7 + 38497*T2^6 + 760*T2^5 - 11613*T2^4 + 159*T2^3 + 1674*T2^2 - 95*T2 - 67