Properties

Label 950.2.h.c
Level $950$
Weight $2$
Character orbit 950.h
Analytic conductor $7.586$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44q - 11q^{2} + q^{3} - 11q^{4} - q^{5} + q^{6} + 18q^{7} - 11q^{8} - 8q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 44q - 11q^{2} + q^{3} - 11q^{4} - q^{5} + q^{6} + 18q^{7} - 11q^{8} - 8q^{9} + 4q^{10} - q^{11} - 4q^{12} + 2q^{13} + 3q^{14} - 4q^{15} - 11q^{16} + 11q^{17} + 42q^{18} + 11q^{19} - 6q^{20} + 3q^{21} - 6q^{22} - 3q^{23} + 6q^{24} - 11q^{25} + 22q^{26} - 23q^{27} - 12q^{28} + 36q^{29} - 4q^{30} + 11q^{31} + 44q^{32} + 2q^{33} - 19q^{34} + 67q^{35} - 8q^{36} + 3q^{37} + 11q^{38} + 47q^{39} + 4q^{40} + 2q^{41} + 3q^{42} + 70q^{43} - 6q^{44} - 28q^{45} - 8q^{46} - 11q^{47} - 4q^{48} + 22q^{49} + 14q^{50} + 38q^{51} + 2q^{52} - 9q^{53} + 32q^{54} + 8q^{55} - 12q^{56} - 6q^{57} + 36q^{58} - 62q^{59} + 11q^{60} - 28q^{61} - 29q^{62} + 10q^{63} - 11q^{64} - 39q^{65} - 8q^{66} + 25q^{67} + 16q^{68} - 81q^{69} - 43q^{70} - 34q^{71} - 13q^{72} + 6q^{73} + 8q^{74} - 39q^{75} - 44q^{76} - 21q^{77} - 58q^{78} + 19q^{79} - q^{80} - 22q^{81} + 2q^{82} - 50q^{83} - 7q^{84} + 102q^{85} - 10q^{86} + 47q^{87} - q^{88} - 4q^{89} - 38q^{90} - 8q^{91} - 8q^{92} + 60q^{93} - 11q^{94} - 4q^{95} + q^{96} + 8q^{97} + 7q^{98} - 12q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
191.1 −0.809017 0.587785i −0.924522 2.84539i 0.309017 + 0.951057i 2.23604 + 0.0110743i −0.924522 + 2.84539i 2.08675 0.309017 0.951057i −4.81444 + 3.49789i −1.80249 1.32327i
191.2 −0.809017 0.587785i −0.636317 1.95838i 0.309017 + 0.951057i 0.252836 + 2.22173i −0.636317 + 1.95838i −0.354998 0.309017 0.951057i −1.00331 + 0.728944i 1.10135 1.94603i
191.3 −0.809017 0.587785i −0.474004 1.45883i 0.309017 + 0.951057i −1.96596 + 1.06536i −0.474004 + 1.45883i −4.21471 0.309017 0.951057i 0.523533 0.380369i 2.21670 + 0.293674i
191.4 −0.809017 0.587785i −0.351062 1.08046i 0.309017 + 0.951057i −0.646677 2.14052i −0.351062 + 1.08046i −1.02053 0.309017 0.951057i 1.38291 1.00474i −0.734991 + 2.11182i
191.5 −0.809017 0.587785i −0.207743 0.639367i 0.309017 + 0.951057i 2.21783 0.285024i −0.207743 + 0.639367i 0.622457 0.309017 0.951057i 2.06142 1.49771i −1.96179 1.07302i
191.6 −0.809017 0.587785i 0.142630 + 0.438971i 0.309017 + 0.951057i −2.07094 + 0.843327i 0.142630 0.438971i 3.64236 0.309017 0.951057i 2.25470 1.63813i 2.17112 + 0.535003i
191.7 −0.809017 0.587785i 0.429059 + 1.32051i 0.309017 + 0.951057i −1.05485 1.97162i 0.429059 1.32051i −3.34366 0.309017 0.951057i 0.867401 0.630204i −0.305496 + 2.21510i
191.8 −0.809017 0.587785i 0.445121 + 1.36994i 0.309017 + 0.951057i −0.223480 + 2.22487i 0.445121 1.36994i −0.156892 0.309017 0.951057i 0.748443 0.543776i 1.48855 1.66860i
191.9 −0.809017 0.587785i 0.549973 + 1.69264i 0.309017 + 0.951057i 1.41010 1.73540i 0.549973 1.69264i 4.16162 0.309017 0.951057i −0.135515 + 0.0984577i −2.16084 + 0.575134i
191.10 −0.809017 0.587785i 0.862591 + 2.65478i 0.309017 + 0.951057i 1.23726 + 1.86257i 0.862591 2.65478i 2.25004 0.309017 0.951057i −3.87675 + 2.81662i 0.0938288 2.23410i
191.11 −0.809017 0.587785i 0.973291 + 2.99548i 0.309017 + 0.951057i −2.20117 + 0.393528i 0.973291 2.99548i −2.52654 0.309017 0.951057i −5.59856 + 4.06759i 2.01209 + 0.975442i
381.1 0.309017 + 0.951057i −2.41843 + 1.75709i −0.809017 + 0.587785i −0.597004 2.15490i −2.41843 1.75709i 1.43148 −0.809017 0.587785i 1.83438 5.64563i 1.86495 1.23368i
381.2 0.309017 + 0.951057i −1.83642 + 1.33424i −0.809017 + 0.587785i −1.65745 + 1.50096i −1.83642 1.33424i 4.52091 −0.809017 0.587785i 0.665206 2.04729i −1.93967 1.11250i
381.3 0.309017 + 0.951057i −1.61479 + 1.17321i −0.809017 + 0.587785i 1.68004 + 1.47562i −1.61479 1.17321i 0.288481 −0.809017 0.587785i 0.304065 0.935817i −0.884238 + 2.05381i
381.4 0.309017 + 0.951057i −1.31294 + 0.953908i −0.809017 + 0.587785i −2.03947 + 0.916822i −1.31294 0.953908i −4.02398 −0.809017 0.587785i −0.113176 + 0.348320i −1.50218 1.65634i
381.5 0.309017 + 0.951057i −0.346707 + 0.251897i −0.809017 + 0.587785i 2.01954 0.959919i −0.346707 0.251897i −2.51273 −0.809017 0.587785i −0.870298 + 2.67850i 1.53701 + 1.62407i
381.6 0.309017 + 0.951057i −0.334955 + 0.243359i −0.809017 + 0.587785i 1.00269 + 1.99865i −0.334955 0.243359i 2.56738 −0.809017 0.587785i −0.874080 + 2.69014i −1.59098 + 1.57124i
381.7 0.309017 + 0.951057i 0.380239 0.276260i −0.809017 + 0.587785i 1.10489 1.94402i 0.380239 + 0.276260i 4.66404 −0.809017 0.587785i −0.858789 + 2.64308i 2.19030 + 0.450073i
381.8 0.309017 + 0.951057i 0.521494 0.378888i −0.809017 + 0.587785i −0.491086 2.18148i 0.521494 + 0.378888i −2.52980 −0.809017 0.587785i −0.798651 + 2.45799i 1.92295 1.14116i
381.9 0.309017 + 0.951057i 1.89683 1.37812i −0.809017 + 0.587785i 1.73578 1.40963i 1.89683 + 1.37812i 2.10540 −0.809017 0.587785i 0.771670 2.37496i 1.87702 + 1.21523i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 761.11
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.2.h.c 44
25.d even 5 1 inner 950.2.h.c 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.2.h.c 44 1.a even 1 1 trivial
950.2.h.c 44 25.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{44} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).