# Properties

 Label 17.10.c.a Level $17$ Weight $10$ Character orbit 17.c Analytic conductor $8.756$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$17$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 17.c (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.75560921479$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q + 144q^{3} - 5124q^{4} - 1710q^{5} - 8174q^{6} + 3810q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q + 144q^{3} - 5124q^{4} - 1710q^{5} - 8174q^{6} + 3810q^{7} + 21946q^{10} + 18132q^{11} - 95142q^{12} + 244832q^{13} - 341100q^{14} - 279932q^{16} - 98022q^{17} + 888764q^{18} + 1364262q^{20} - 775748q^{21} - 4573190q^{22} - 377526q^{23} - 307054q^{24} + 3996108q^{27} - 1024780q^{28} + 2160042q^{29} + 39084792q^{30} - 585086q^{31} - 30349992q^{33} + 4441318q^{34} - 25532364q^{35} + 1515390q^{37} + 13171392q^{38} - 25687084q^{39} - 63240118q^{40} - 72707928q^{41} - 3606450q^{44} + 156729418q^{45} + 118549536q^{46} + 153365328q^{47} + 26098270q^{48} - 236105676q^{50} + 256903592q^{51} - 209898380q^{52} - 187411976q^{54} + 255767540q^{55} - 107638596q^{56} - 443390988q^{57} - 281433730q^{58} + 52149382q^{61} + 176928228q^{62} + 620111642q^{63} + 1006108924q^{64} - 489714396q^{65} - 26076868q^{67} - 308011950q^{68} - 751973532q^{69} + 149240178q^{71} + 1171736028q^{72} - 175256556q^{73} - 37609818q^{74} - 233543476q^{75} - 1202722924q^{78} - 469987182q^{79} + 481103586q^{80} + 347156560q^{81} - 984422080q^{82} - 935672904q^{84} - 725828294q^{85} + 690159588q^{86} + 992281114q^{88} - 191594460q^{89} + 914946474q^{90} + 926854816q^{91} + 3064830552q^{92} + 1213246572q^{95} + 3594247550q^{96} - 2200567348q^{97} - 4413444720q^{98} - 1224966600q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
4.1 38.1697i −95.6730 + 95.6730i −944.927 −23.8207 + 23.8207i 3651.81 + 3651.81i 3405.47 + 3405.47i 16524.7i 1376.34i 909.229 + 909.229i
4.2 36.7615i 151.130 151.130i −839.411 −1546.81 + 1546.81i −5555.78 5555.78i −1021.13 1021.13i 12036.1i 25997.7i 56863.1 + 56863.1i
4.3 31.4159i 42.7255 42.7255i −474.957 1118.79 1118.79i −1342.26 1342.26i −7416.51 7416.51i 1163.73i 16032.1i −35147.8 35147.8i
4.4 17.1503i 97.3786 97.3786i 217.866 882.390 882.390i −1670.08 1670.08i 7460.78 + 7460.78i 12517.4i 717.820i −15133.3 15133.3i
4.5 12.8587i −144.765 + 144.765i 346.654 −85.3199 + 85.3199i 1861.49 + 1861.49i −3200.21 3200.21i 11041.2i 22230.9i 1097.10 + 1097.10i
4.6 9.57683i −2.66069 + 2.66069i 420.284 −1324.59 + 1324.59i 25.4810 + 25.4810i 1098.57 + 1098.57i 8928.33i 19668.8i 12685.3 + 12685.3i
4.7 7.42963i 150.879 150.879i 456.801 210.983 210.983i 1120.97 + 1120.97i −5461.47 5461.47i 7197.83i 25845.7i 1567.53 + 1567.53i
4.8 12.9147i −71.7165 + 71.7165i 345.210 1469.78 1469.78i −926.198 926.198i 1528.49 + 1528.49i 11070.6i 9396.49i 18981.8 + 18981.8i
4.9 21.4252i 22.6833 22.6833i 52.9591 −1056.12 + 1056.12i 485.995 + 485.995i −862.967 862.967i 12104.4i 18653.9i −22627.6 22627.6i
4.10 28.8329i −179.389 + 179.389i −319.336 −1133.17 + 1133.17i −5172.29 5172.29i 4922.20 + 4922.20i 5555.06i 44677.5i −32672.5 32672.5i
4.11 35.4517i 137.825 137.825i −744.825 178.043 178.043i 4886.12 + 4886.12i 7491.11 + 7491.11i 8254.04i 18308.3i 6311.91 + 6311.91i
4.12 39.8788i −36.4169 + 36.4169i −1078.32 454.832 454.832i −1452.26 1452.26i −6039.34 6039.34i 22584.0i 17030.6i 18138.1 + 18138.1i
13.1 39.8788i −36.4169 36.4169i −1078.32 454.832 + 454.832i −1452.26 + 1452.26i −6039.34 + 6039.34i 22584.0i 17030.6i 18138.1 18138.1i
13.2 35.4517i 137.825 + 137.825i −744.825 178.043 + 178.043i 4886.12 4886.12i 7491.11 7491.11i 8254.04i 18308.3i 6311.91 6311.91i
13.3 28.8329i −179.389 179.389i −319.336 −1133.17 1133.17i −5172.29 + 5172.29i 4922.20 4922.20i 5555.06i 44677.5i −32672.5 + 32672.5i
13.4 21.4252i 22.6833 + 22.6833i 52.9591 −1056.12 1056.12i 485.995 485.995i −862.967 + 862.967i 12104.4i 18653.9i −22627.6 + 22627.6i
13.5 12.9147i −71.7165 71.7165i 345.210 1469.78 + 1469.78i −926.198 + 926.198i 1528.49 1528.49i 11070.6i 9396.49i 18981.8 18981.8i
13.6 7.42963i 150.879 + 150.879i 456.801 210.983 + 210.983i 1120.97 1120.97i −5461.47 + 5461.47i 7197.83i 25845.7i 1567.53 1567.53i
13.7 9.57683i −2.66069 2.66069i 420.284 −1324.59 1324.59i 25.4810 25.4810i 1098.57 1098.57i 8928.33i 19668.8i 12685.3 12685.3i
13.8 12.8587i −144.765 144.765i 346.654 −85.3199 85.3199i 1861.49 1861.49i −3200.21 + 3200.21i 11041.2i 22230.9i 1097.10 1097.10i
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 13.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

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

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 17.10.c.a 24
17.c even 4 1 inner 17.10.c.a 24
17.d even 8 2 289.10.a.f 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.10.c.a 24 1.a even 1 1 trivial
17.10.c.a 24 17.c even 4 1 inner
289.10.a.f 24 17.d even 8 2

## Hecke kernels

This newform subspace is the entire newspace $$S_{10}^{\mathrm{new}}(17, [\chi])$$.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database