# Properties

 Label 1155.2.k.b Level 1155 Weight 2 Character orbit 1155.k Analytic conductor 9.223 Analytic rank 0 Dimension 48 CM No

# Related objects

## Newspace parameters

 Level: $$N$$ = $$1155 = 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1155.k (of order $$2$$ and degree $$1$$)

## Newform invariants

 Self dual: No Analytic conductor: $$9.22272143346$$ Analytic rank: $$0$$ Dimension: $$48$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$48q$$ $$\mathstrut +\mathstrut 48q^{3}$$ $$\mathstrut +\mathstrut 48q^{4}$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut +\mathstrut 48q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$48q$$ $$\mathstrut +\mathstrut 48q^{3}$$ $$\mathstrut +\mathstrut 48q^{4}$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut +\mathstrut 48q^{9}$$ $$\mathstrut +\mathstrut 48q^{12}$$ $$\mathstrut -\mathstrut 4q^{15}$$ $$\mathstrut +\mathstrut 40q^{16}$$ $$\mathstrut -\mathstrut 18q^{20}$$ $$\mathstrut +\mathstrut 20q^{25}$$ $$\mathstrut +\mathstrut 48q^{27}$$ $$\mathstrut +\mathstrut 48q^{36}$$ $$\mathstrut -\mathstrut 20q^{38}$$ $$\mathstrut -\mathstrut 16q^{44}$$ $$\mathstrut -\mathstrut 4q^{45}$$ $$\mathstrut +\mathstrut 8q^{47}$$ $$\mathstrut +\mathstrut 40q^{48}$$ $$\mathstrut +\mathstrut 24q^{49}$$ $$\mathstrut -\mathstrut 8q^{55}$$ $$\mathstrut -\mathstrut 8q^{56}$$ $$\mathstrut -\mathstrut 18q^{60}$$ $$\mathstrut -\mathstrut 4q^{64}$$ $$\mathstrut -\mathstrut 14q^{70}$$ $$\mathstrut -\mathstrut 32q^{71}$$ $$\mathstrut +\mathstrut 20q^{75}$$ $$\mathstrut -\mathstrut 32q^{77}$$ $$\mathstrut -\mathstrut 46q^{80}$$ $$\mathstrut +\mathstrut 48q^{81}$$ $$\mathstrut -\mathstrut 32q^{82}$$ $$\mathstrut -\mathstrut 16q^{86}$$ $$\mathstrut +\mathstrut 68q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
769.1 −2.66471 1.00000 5.10065 −1.18527 1.89608i −2.66471 2.09935 + 1.61019i −8.26233 1.00000 3.15840 + 5.05250i
769.2 −2.66471 1.00000 5.10065 −1.18527 + 1.89608i −2.66471 2.09935 1.61019i −8.26233 1.00000 3.15840 5.05250i
769.3 −2.52930 1.00000 4.39737 −1.63381 1.52665i −2.52930 −2.48590 0.905718i −6.06368 1.00000 4.13240 + 3.86136i
769.4 −2.52930 1.00000 4.39737 −1.63381 + 1.52665i −2.52930 −2.48590 + 0.905718i −6.06368 1.00000 4.13240 3.86136i
769.5 −2.43104 1.00000 3.90997 2.21714 + 0.290295i −2.43104 1.43522 + 2.22265i −4.64322 1.00000 −5.38997 0.705719i
769.6 −2.43104 1.00000 3.90997 2.21714 0.290295i −2.43104 1.43522 2.22265i −4.64322 1.00000 −5.38997 + 0.705719i
769.7 −2.15215 1.00000 2.63174 1.03706 1.98104i −2.15215 −2.36665 1.18277i −1.35961 1.00000 −2.23191 + 4.26348i
769.8 −2.15215 1.00000 2.63174 1.03706 + 1.98104i −2.15215 −2.36665 + 1.18277i −1.35961 1.00000 −2.23191 4.26348i
769.9 −1.83264 1.00000 1.35857 0.538446 2.17027i −1.83264 −0.996474 + 2.45093i 1.17551 1.00000 −0.986778 + 3.97732i
769.10 −1.83264 1.00000 1.35857 0.538446 + 2.17027i −1.83264 −0.996474 2.45093i 1.17551 1.00000 −0.986778 3.97732i
769.11 −1.69546 1.00000 0.874594 −2.22547 0.217459i −1.69546 0.698105 2.55199i 1.90808 1.00000 3.77320 + 0.368694i
769.12 −1.69546 1.00000 0.874594 −2.22547 + 0.217459i −1.69546 0.698105 + 2.55199i 1.90808 1.00000 3.77320 0.368694i
769.13 −1.63529 1.00000 0.674169 −1.84877 1.25780i −1.63529 1.79271 1.94582i 2.16812 1.00000 3.02327 + 2.05687i
769.14 −1.63529 1.00000 0.674169 −1.84877 + 1.25780i −1.63529 1.79271 + 1.94582i 2.16812 1.00000 3.02327 2.05687i
769.15 −1.17317 1.00000 −0.623669 2.20931 0.344884i −1.17317 −1.71739 + 2.01260i 3.07801 1.00000 −2.59190 + 0.404608i
769.16 −1.17317 1.00000 −0.623669 2.20931 + 0.344884i −1.17317 −1.71739 2.01260i 3.07801 1.00000 −2.59190 0.404608i
769.17 −1.12050 1.00000 −0.744486 1.27295 + 1.83837i −1.12050 2.54893 0.709189i 3.07519 1.00000 −1.42634 2.05989i
769.18 −1.12050 1.00000 −0.744486 1.27295 1.83837i −1.12050 2.54893 + 0.709189i 3.07519 1.00000 −1.42634 + 2.05989i
769.19 −0.567201 1.00000 −1.67828 −2.10264 0.760858i −0.567201 −2.63586 + 0.228555i 2.08633 1.00000 1.19262 + 0.431559i
769.20 −0.567201 1.00000 −1.67828 −2.10264 + 0.760858i −0.567201 −2.63586 0.228555i 2.08633 1.00000 1.19262 0.431559i
See all 48 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 769.48 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not have CM; other inner twists have not been computed.