# Properties

 Label 1150.3.c.c Level $1150$ Weight $3$ Character orbit 1150.c Analytic conductor $31.335$ Analytic rank $0$ Dimension $32$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1150 = 2 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1150.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$31.3352304014$$ Analytic rank: $$0$$ Dimension: $$32$$ Twist minimal: no (minimal twist has level 230) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10})$$ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100})$$ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1149.1 1.41421i 1.43837i −2.00000 0 2.03417 −10.1866 2.82843i 6.93108 0
1149.2 1.41421i 1.43837i −2.00000 0 2.03417 −10.1866 2.82843i 6.93108 0
1149.3 1.41421i 5.41949i −2.00000 0 7.66432 8.24199 2.82843i −20.3709 0
1149.4 1.41421i 5.41949i −2.00000 0 7.66432 8.24199 2.82843i −20.3709 0
1149.5 1.41421i 4.76369i −2.00000 0 −6.73687 −7.05858 2.82843i −13.6927 0
1149.6 1.41421i 4.76369i −2.00000 0 −6.73687 −7.05858 2.82843i −13.6927 0
1149.7 1.41421i 0.278523i −2.00000 0 0.393890 8.51262 2.82843i 8.92243 0
1149.8 1.41421i 0.278523i −2.00000 0 0.393890 8.51262 2.82843i 8.92243 0
1149.9 1.41421i 3.79379i −2.00000 0 −5.36524 −7.10180 2.82843i −5.39287 0
1149.10 1.41421i 3.79379i −2.00000 0 −5.36524 −7.10180 2.82843i −5.39287 0
1149.11 1.41421i 2.34854i −2.00000 0 −3.32134 7.61815 2.82843i 3.48436 0
1149.12 1.41421i 2.34854i −2.00000 0 −3.32134 7.61815 2.82843i 3.48436 0
1149.13 1.41421i 4.30716i −2.00000 0 6.09125 −1.47532 2.82843i −9.55167 0
1149.14 1.41421i 4.30716i −2.00000 0 6.09125 −1.47532 2.82843i −9.55167 0
1149.15 1.41421i 3.36596i −2.00000 0 −4.76019 1.16919 2.82843i −2.32968 0
1149.16 1.41421i 3.36596i −2.00000 0 −4.76019 1.16919 2.82843i −2.32968 0
1149.17 1.41421i 3.36596i −2.00000 0 −4.76019 −1.16919 2.82843i −2.32968 0
1149.18 1.41421i 3.36596i −2.00000 0 −4.76019 −1.16919 2.82843i −2.32968 0
1149.19 1.41421i 4.30716i −2.00000 0 6.09125 1.47532 2.82843i −9.55167 0
1149.20 1.41421i 4.30716i −2.00000 0 6.09125 1.47532 2.82843i −9.55167 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1149.32 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
23.b odd 2 1 inner
115.c odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1150.3.c.c 32
5.b even 2 1 inner 1150.3.c.c 32
5.c odd 4 1 230.3.d.a 16
5.c odd 4 1 1150.3.d.b 16
15.e even 4 1 2070.3.c.a 16
20.e even 4 1 1840.3.k.d 16
23.b odd 2 1 inner 1150.3.c.c 32
115.c odd 2 1 inner 1150.3.c.c 32
115.e even 4 1 230.3.d.a 16
115.e even 4 1 1150.3.d.b 16
345.l odd 4 1 2070.3.c.a 16
460.k odd 4 1 1840.3.k.d 16

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.3.d.a 16 5.c odd 4 1
230.3.d.a 16 115.e even 4 1
1150.3.c.c 32 1.a even 1 1 trivial
1150.3.c.c 32 5.b even 2 1 inner
1150.3.c.c 32 23.b odd 2 1 inner
1150.3.c.c 32 115.c odd 2 1 inner
1150.3.d.b 16 5.c odd 4 1
1150.3.d.b 16 115.e even 4 1
1840.3.k.d 16 20.e even 4 1
1840.3.k.d 16 460.k odd 4 1
2070.3.c.a 16 15.e even 4 1
2070.3.c.a 16 345.l odd 4 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{16} + 104 T_{3}^{14} + 4362 T_{3}^{12} + 94700 T_{3}^{10} + 1132361 T_{3}^{8} + 7286420 T_{3}^{6} + 22518132 T_{3}^{4} + 24712224 T_{3}^{2} + 1784896$$ acting on $$S_{3}^{\mathrm{new}}(1150, [\chi])$$.