Properties

Label 950.2.bb.c
Level $950$
Weight $2$
Character orbit 950.bb
Analytic conductor $7.586$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72q + 24q^{6} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 72q + 24q^{6} + 24q^{21} + 12q^{26} + 36q^{31} - 24q^{36} + 48q^{41} - 36q^{46} + 156q^{51} + 168q^{61} - 36q^{66} - 84q^{71} - 48q^{76} - 60q^{81} - 60q^{86} - 264q^{91} + 24q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
143.1 −0.573576 + 0.819152i −0.181419 + 2.07363i −0.342020 0.939693i 0 −1.59456 1.33799i 1.21655 + 4.54023i 0.965926 + 0.258819i −1.31260 0.231446i 0
143.2 −0.573576 + 0.819152i 0.00886944 0.101378i −0.342020 0.939693i 0 0.0779568 + 0.0654135i −0.0402147 0.150083i 0.965926 + 0.258819i 2.94422 + 0.519146i 0
143.3 −0.573576 + 0.819152i 0.218924 2.50231i −0.342020 0.939693i 0 1.92421 + 1.61460i 0.801272 + 2.99039i 0.965926 + 0.258819i −3.25922 0.574689i 0
143.4 0.573576 0.819152i −0.218924 + 2.50231i −0.342020 0.939693i 0 1.92421 + 1.61460i −0.801272 2.99039i −0.965926 0.258819i −3.25922 0.574689i 0
143.5 0.573576 0.819152i −0.00886944 + 0.101378i −0.342020 0.939693i 0 0.0779568 + 0.0654135i 0.0402147 + 0.150083i −0.965926 0.258819i 2.94422 + 0.519146i 0
143.6 0.573576 0.819152i 0.181419 2.07363i −0.342020 0.939693i 0 −1.59456 1.33799i −1.21655 4.54023i −0.965926 0.258819i −1.31260 0.231446i 0
193.1 −0.0871557 0.996195i −1.14235 + 2.44977i −0.984808 + 0.173648i 0 2.54001 + 0.924487i −1.86007 0.498404i 0.258819 + 0.965926i −2.76804 3.29882i 0
193.2 −0.0871557 0.996195i −0.475045 + 1.01874i −0.984808 + 0.173648i 0 1.05626 + 0.384448i 3.66894 + 0.983089i 0.258819 + 0.965926i 1.11621 + 1.33024i 0
193.3 −0.0871557 0.996195i 0.400509 0.858895i −0.984808 + 0.173648i 0 −0.890533 0.324128i 0.243409 + 0.0652212i 0.258819 + 0.965926i 1.35107 + 1.61014i 0
193.4 0.0871557 + 0.996195i −0.400509 + 0.858895i −0.984808 + 0.173648i 0 −0.890533 0.324128i −0.243409 0.0652212i −0.258819 0.965926i 1.35107 + 1.61014i 0
193.5 0.0871557 + 0.996195i 0.475045 1.01874i −0.984808 + 0.173648i 0 1.05626 + 0.384448i −3.66894 0.983089i −0.258819 0.965926i 1.11621 + 1.33024i 0
193.6 0.0871557 + 0.996195i 1.14235 2.44977i −0.984808 + 0.173648i 0 2.54001 + 0.924487i 1.86007 + 0.498404i −0.258819 0.965926i −2.76804 3.29882i 0
243.1 −0.422618 0.906308i −2.29045 1.60379i −0.642788 + 0.766044i 0 −0.485541 + 2.75364i 0.367125 + 1.37013i 0.965926 + 0.258819i 1.64795 + 4.52771i 0
243.2 −0.422618 0.906308i −0.0850875 0.0595789i −0.642788 + 0.766044i 0 −0.0180373 + 0.102295i 0.497281 + 1.85588i 0.965926 + 0.258819i −1.02237 2.80894i 0
243.3 −0.422618 0.906308i 1.84087 + 1.28899i −0.642788 + 0.766044i 0 0.390238 2.21315i −0.947246 3.53517i 0.965926 + 0.258819i 0.701247 + 1.92666i 0
243.4 0.422618 + 0.906308i −1.84087 1.28899i −0.642788 + 0.766044i 0 0.390238 2.21315i 0.947246 + 3.53517i −0.965926 0.258819i 0.701247 + 1.92666i 0
243.5 0.422618 + 0.906308i 0.0850875 + 0.0595789i −0.642788 + 0.766044i 0 −0.0180373 + 0.102295i −0.497281 1.85588i −0.965926 0.258819i −1.02237 2.80894i 0
243.6 0.422618 + 0.906308i 2.29045 + 1.60379i −0.642788 + 0.766044i 0 −0.485541 + 2.75364i −0.367125 1.37013i −0.965926 0.258819i 1.64795 + 4.52771i 0
257.1 −0.819152 0.573576i −2.50231 0.218924i 0.342020 + 0.939693i 0 1.92421 + 1.61460i −2.99039 + 0.801272i 0.258819 0.965926i 3.25922 + 0.574689i 0
257.2 −0.819152 0.573576i −0.101378 0.00886944i 0.342020 + 0.939693i 0 0.0779568 + 0.0654135i 0.150083 0.0402147i 0.258819 0.965926i −2.94422 0.519146i 0
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 907.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
5.c odd 4 2 inner
19.f odd 18 1 inner
95.o odd 18 1 inner
95.r even 36 2 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.2.bb.c 72
5.b even 2 1 inner 950.2.bb.c 72
5.c odd 4 2 inner 950.2.bb.c 72
19.f odd 18 1 inner 950.2.bb.c 72
95.o odd 18 1 inner 950.2.bb.c 72
95.r even 36 2 inner 950.2.bb.c 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.2.bb.c 72 1.a even 1 1 trivial
950.2.bb.c 72 5.b even 2 1 inner
950.2.bb.c 72 5.c odd 4 2 inner
950.2.bb.c 72 19.f odd 18 1 inner
950.2.bb.c 72 95.o odd 18 1 inner
950.2.bb.c 72 95.r even 36 2 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(40\!\cdots\!80\)\( T_{3}^{40} - \)\(21\!\cdots\!40\)\( T_{3}^{36} + \)\(36\!\cdots\!82\)\( T_{3}^{32} + \)\(25\!\cdots\!04\)\( T_{3}^{28} + \)\(12\!\cdots\!86\)\( T_{3}^{24} + \)\(38\!\cdots\!04\)\( T_{3}^{20} + \)\(64\!\cdots\!37\)\( T_{3}^{16} - 148923767649 T_{3}^{12} - 69896577 T_{3}^{8} - 4362 T_{3}^{4} + 1 \)">\(T_{3}^{72} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).