Properties

 Label 276.1.h.b Level 276 Weight 1 Character orbit 276.h Self dual Yes Analytic conductor 0.138 Analytic rank 0 Dimension 1 Projective image $$D_{2}$$ CM/RM disc. -23, -276, 12 Inner twists 4

Related objects

Newspace parameters

 Level: $$N$$ = $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 276.h (of order $$2$$ and degree $$1$$)

Newform invariants

 Self dual: Yes Analytic conductor: $$0.137741943487$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Projective image $$D_{2}$$ Projective field Galois closure of $$\Q(\sqrt{3}, \sqrt{-23})$$ Artin image size $$8$$ Artin image $D_4$ Artin field Galois closure of 4.2.3312.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + O(q^{10})$$ $$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{12} - 2q^{13} + q^{16} + q^{18} - q^{23} - q^{24} - q^{25} - 2q^{26} - q^{27} + q^{32} + q^{36} + 2q^{39} - q^{46} + 2q^{47} - q^{48} - q^{49} - q^{50} - 2q^{52} - q^{54} + 2q^{59} + q^{64} + q^{69} - 2q^{71} + q^{72} + 2q^{73} + q^{75} + 2q^{78} + q^{81} - q^{92} + 2q^{94} - q^{96} - q^{98} + O(q^{100})$$

Character Values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$139$$ $$185$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
275.1
 0
1.00000 −1.00000 1.00000 0 −1.00000 0 1.00000 1.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
12.b Even 1 RM by $$\Q(\sqrt{3})$$ yes
23.b Odd 1 CM by $$\Q(\sqrt{-23})$$ yes
276.h Odd 1 CM by $$\Q(\sqrt{-69})$$ yes

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{1}^{\mathrm{new}}(276, [\chi])$$:

 $$T_{13} + 2$$ $$T_{47} - 2$$