# Properties

 Label 46.2.c.b Level $46$ Weight $2$ Character orbit 46.c Analytic conductor $0.367$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$46 = 2 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 46.c (of order $$11$$, degree $$10$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.367311849298$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\Q(\zeta_{22})$$ Defining polynomial: $$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{22}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + \zeta_{22} q^{2} + (\zeta_{22}^{9} + \zeta_{22}^{7} + \zeta_{22}^{4} - \zeta_{22}) q^{3} + \zeta_{22}^{2} q^{4} + ( - \zeta_{22}^{9} - \zeta_{22}^{7} - \zeta_{22}^{5} - \zeta_{22}^{3}) q^{5} + (\zeta_{22}^{9} + \zeta_{22}^{7} - \zeta_{22}^{6} + 2 \zeta_{22}^{5} - \zeta_{22}^{4} + \zeta_{22}^{3} - 2 \zeta_{22}^{2} + \zeta_{22} - 1) q^{6} + ( - 2 \zeta_{22}^{8} + \zeta_{22}^{7} - \zeta_{22}^{6} + 2 \zeta_{22}^{5} - 3 \zeta_{22}^{4} + 2 \zeta_{22}^{3} - \zeta_{22}^{2} + \cdots - 2) q^{7}+ \cdots + ( - 2 \zeta_{22}^{9} + \zeta_{22}^{8} - 3 \zeta_{22}^{7} + 2 \zeta_{22}^{6} - 3 \zeta_{22}^{5} + 2 \zeta_{22}^{4} + \cdots - 2 \zeta_{22}) q^{9}+O(q^{10})$$ q + z * q^2 + (z^9 + z^7 + z^4 - z) * q^3 + z^2 * q^4 + (-z^9 - z^7 - z^5 - z^3) * q^5 + (z^9 + z^7 - z^6 + 2*z^5 - z^4 + z^3 - 2*z^2 + z - 1) * q^6 + (-2*z^8 + z^7 - z^6 + 2*z^5 - 3*z^4 + 2*z^3 - z^2 + z - 2) * q^7 + z^3 * q^8 + (-2*z^9 + z^8 - 3*z^7 + 2*z^6 - 3*z^5 + 2*z^4 - 3*z^3 + z^2 - 2*z) * q^9 $$q + \zeta_{22} q^{2} + (\zeta_{22}^{9} + \zeta_{22}^{7} + \zeta_{22}^{4} - \zeta_{22}) q^{3} + \zeta_{22}^{2} q^{4} + ( - \zeta_{22}^{9} - \zeta_{22}^{7} - \zeta_{22}^{5} - \zeta_{22}^{3}) q^{5} + (\zeta_{22}^{9} + \zeta_{22}^{7} - \zeta_{22}^{6} + 2 \zeta_{22}^{5} - \zeta_{22}^{4} + \zeta_{22}^{3} - 2 \zeta_{22}^{2} + \zeta_{22} - 1) q^{6} + ( - 2 \zeta_{22}^{8} + \zeta_{22}^{7} - \zeta_{22}^{6} + 2 \zeta_{22}^{5} - 3 \zeta_{22}^{4} + 2 \zeta_{22}^{3} - \zeta_{22}^{2} + \cdots - 2) q^{7}+ \cdots + (\zeta_{22}^{8} + \zeta_{22}^{7} + 2 \zeta_{22}^{6} - \zeta_{22}^{5} - \zeta_{22}^{4} - \zeta_{22}^{3} + 2 \zeta_{22}^{2} + \zeta_{22} + 1) q^{99}+O(q^{100})$$ q + z * q^2 + (z^9 + z^7 + z^4 - z) * q^3 + z^2 * q^4 + (-z^9 - z^7 - z^5 - z^3) * q^5 + (z^9 + z^7 - z^6 + 2*z^5 - z^4 + z^3 - 2*z^2 + z - 1) * q^6 + (-2*z^8 + z^7 - z^6 + 2*z^5 - 3*z^4 + 2*z^3 - z^2 + z - 2) * q^7 + z^3 * q^8 + (-2*z^9 + z^8 - 3*z^7 + 2*z^6 - 3*z^5 + 2*z^4 - 3*z^3 + z^2 - 2*z) * q^9 + (-z^9 - z^7 - z^5 - z^3 + z^2 - z + 1) * q^10 + (z^8 - z^6 - z^5 + z^4 + z^3 - z) * q^11 + (z^9 + z^6 - z^3 - 1) * q^12 + (z^9 + 3*z^8 - z^7 + 3*z^6 + z^5 - z^3 + z^2 - z + 1) * q^13 + (-2*z^9 + z^8 - z^7 + 2*z^6 - 3*z^5 + 2*z^4 - z^3 + z^2 - 2*z) * q^14 + (-z^9 + z^8 + z^6 + 2*z^5 + z^4 + 2*z^3 + z^2 + 2*z + 1) * q^15 + z^4 * q^16 + (z^9 + 2*z^7 - 3*z^6 - z^4 + z^3 + 3*z - 2) * q^17 + (-z^9 - z^8 - z^6 - z^4 - z^3 - 2*z + 2) * q^18 + (z^9 - 3*z^8 + 3*z^7 - z^6 - z^4 - 3*z^2 - 1) * q^19 + (-z^9 - z^7 - z^5 + 1) * q^20 + (3*z^9 - 5*z^8 + 3*z^7 - 3*z^6 + 5*z^5 - 3*z^4 + z^2 + 2*z + 1) * q^21 + (z^9 - z^7 - z^6 + z^5 + z^4 - z^2) * q^22 + (z^9 - z^8 - z^7 - 2*z^6 + 3*z^3 - 2*z^2 + 3*z + 1) * q^23 + (z^9 - z^8 + 2*z^7 - z^6 + z^5 - 2*z^4 + z^3 - z^2 - 1) * q^24 + (3*z^9 - z^8 + 2*z^7 - 2*z^6 + z^5 - 3*z^4 - 3*z^2 + 4*z - 3) * q^25 + (4*z^9 - 2*z^8 + 4*z^7 + z^5 - 2*z^4 + 2*z^3 - 2*z^2 + 2*z - 1) * q^26 + (-z^9 + 4*z^8 - 4*z^7 + z^6 + z^4 + z^3 + z^2 + z + 1) * q^27 + (-z^9 + z^8 - z^6 + z^4 - z^3 - 2*z + 2) * q^28 + (-4*z^9 - 2*z^7 + 3*z^6 - 2*z^5 + 3*z^4 - 3*z^3 + 2*z^2 - 3*z + 2) * q^29 + (z^8 + 3*z^6 + 3*z^4 + 3*z^2 + 1) * q^30 + (-3*z^9 + 3*z^8 + 4*z^6 - 4*z^5 + 4*z^4 - 3*z^3 + 4*z^2 - 4*z + 4) * q^31 + z^5 * q^32 + (-3*z^9 + z^8 + z^7 + z^6 - 3*z^5 + 2*z^2 - 2*z) * q^33 + (z^9 + z^8 - 2*z^7 - z^6 + z^3 + 2*z^2 - z - 1) * q^34 + (z^9 + z^8 + z^6 - 2*z^5 + 2*z^4 - z^3 - z - 1) * q^35 + (-2*z^9 + z^8 - 2*z^7 + z^6 - 2*z^5 - z^3 - z^2 + z + 1) * q^36 + (-z^9 + 3*z^8 - 2*z^7 + 4*z^6 + 2*z^5 + 4*z^4 - 2*z^3 + 3*z^2 - z) * q^37 + (-2*z^9 + 2*z^8 - z^6 - z^4 - 2*z^3 - z^2 - 1) * q^38 + (-4*z^7 - 3*z^6 - z^5 - 4*z^4 - z^3 - 3*z^2 - 4*z) * q^39 + (-z^9 - z^7 - z^5 + z^4 - z^3 + z^2 + 1) * q^40 + (z^9 - 3*z^7 - 3*z^5 + z^3 - z + 1) * q^41 + (-2*z^9 + 2*z^6 - 3*z^4 + 4*z^3 - z^2 + 4*z - 3) * q^42 + (3*z^9 - 8*z^8 + 3*z^7 + 5*z^5 - 2*z^4 + 3*z^3 - 3*z^2 + 2*z - 5) * q^43 + (z^9 - 2*z^8 + 2*z^5 - z^4 - z^2 + z - 1) * q^44 + (6*z^9 - 3*z^8 + 6*z^7 - 5*z^6 + 5*z^5 - 6*z^4 + 3*z^3 - 6*z^2 - 5) * q^45 + (-2*z^8 - z^7 - z^6 + z^5 + 2*z^4 - z^3 + 2*z^2 + 2*z - 1) * q^46 + (-2*z^9 + 4*z^7 - 2*z^6 + 2*z^5 - 4*z^4 + 2*z^2 - 3) * q^47 + (z^8 - z^5 - z^2 - 1) * q^48 + (-4*z^9 + 4*z^8 - 4*z^7 - 4*z^5 + 3*z^4 + 3*z^3 - 3*z^2 - 3*z + 4) * q^49 + (2*z^9 - z^8 + z^7 - 2*z^6 - 3*z^4 + z^2 - 3) * q^50 + (-2*z^9 + z^7 + z^5 - 2*z^3 + z - 1) * q^51 + (2*z^9 + 4*z^7 - 3*z^6 + 2*z^5 - 2*z^4 + 2*z^3 - 2*z^2 + 3*z - 4) * q^52 + (-3*z^7 + z^4 - 3*z) * q^53 + (3*z^9 - 3*z^8 + z^6 + 2*z^4 + 2*z^2 + 1) * q^54 + (z^9 + z^5 + z) * q^55 + (z^8 - 2*z^7 + z^6 - z^3 - z^2 + z + 1) * q^56 + (-3*z^9 - 2*z^8 - 3*z^7 + 2*z^6 - 5*z^5 + 5*z^4 - 2*z^3 + 3*z^2 + 2*z + 3) * q^57 + (-4*z^9 + 2*z^8 - z^7 + 2*z^6 - z^5 + z^4 - 2*z^3 + z^2 - 2*z + 4) * q^58 + (2*z^8 + z^7 + 2*z^6 - 6*z^3 + 4*z^2 - 4*z + 6) * q^59 + (z^9 + 3*z^7 + 3*z^5 + 3*z^3 + z) * q^60 + (-2*z^9 + 2*z^8 - z^5 - z^4 + z^3 - z^2 - z) * q^61 + (3*z^8 + z^7 - z^6 + z^5 + z^3 - z^2 + z + 3) * q^62 + (5*z^9 + 2*z^6 - 5*z^5 + 7*z^4 - 7*z^3 + 5*z^2 - 2*z) * q^63 + z^6 * q^64 + (-3*z^9 - z^8 + z^7 + 3*z^6 + 5*z^4 + 2*z^3 + 4*z^2 + 2*z + 5) * q^65 + (-2*z^9 + 4*z^8 - 2*z^7 - 3*z^5 + 3*z^4 - z^3 + z^2 - 3*z + 3) * q^66 + (z^9 + 5*z^8 - 3*z^7 + 3*z^6 - 5*z^5 - z^4 + z^2 + 4*z + 1) * q^67 + (2*z^9 - 3*z^8 - z^6 + z^5 + 3*z^3 - 2*z^2 - 1) * q^68 + (3*z^9 + z^8 + 8*z^7 - 4*z^6 + 6*z^5 - 2*z^4 + 6*z^3 - 5*z^2) * q^69 + (2*z^9 - z^8 + 2*z^7 - 3*z^6 + 3*z^5 - 2*z^4 + z^3 - 2*z^2 - 1) * q^70 + (z^9 - z^8 - 3*z^7 + 3*z^6 + z^5 - z^4 - z^2 - 1) * q^71 + (-z^9 - z^7 - 2*z^5 + z^4 - 3*z^3 + 3*z^2 - z + 2) * q^72 + (3*z^9 - 4*z^8 + 4*z^7 - 3*z^6 - 6*z^4 + 5*z^3 - 2*z^2 + 5*z - 6) * q^73 + (2*z^9 - z^8 + 3*z^7 + 3*z^6 + 3*z^5 - z^4 + 2*z^3 - z + 1) * q^74 + (-5*z^9 - 5*z^7 - 2*z^6 + z^5 + z^4 - z^3 - z^2 + 2*z + 5) * q^75 + (2*z^8 - 3*z^7 + 2*z^6 - 3*z^5 - 3*z^3 + 2*z^2 - 3*z + 2) * q^76 + (5*z^9 - 5*z^8 + 7*z^5 - 4*z^4 - 2*z^3 - 4*z^2 + 7*z) * q^77 + (-4*z^8 - 3*z^7 - z^6 - 4*z^5 - z^4 - 3*z^3 - 4*z^2) * q^78 + (-6*z^8 + 5*z^7 - 6*z^6 - z^3 - 4*z^2 + 4*z + 1) * q^79 + (-z^9 - z^7 + z^2 + 1) * q^80 + (-z^9 + 2*z^8 - 4*z^6 + 4*z^3 - 2*z + 1) * q^81 + (z^9 - 4*z^8 + z^7 - 4*z^6 + z^5 + z^3 - 2*z^2 + 2*z - 1) * q^82 + (-3*z^9 + 4*z^8 - z^7 - 5*z^6 + 3*z^5 - 5*z^4 - z^3 + 4*z^2 - 3*z) * q^83 + (-2*z^9 + 2*z^8 + 2*z^6 - 5*z^5 + 6*z^4 - 3*z^3 + 6*z^2 - 5*z + 2) * q^84 + (2*z^8 - 2*z^7 + 2*z^6 - z^5 - z^3 + 2*z^2 - 2*z + 2) * q^85 + (-5*z^9 + 3*z^7 + 2*z^6 + z^5 - z^2 - 2*z - 3) * q^86 + (3*z^9 + z^8 + z^7 + 3*z^6 + z^5 + z^4 + 3*z^3 + 4*z - 4) * q^87 + (-z^9 - z^8 + z^7 + z^6 - z^4 - 1) * q^88 + (4*z^9 + 4*z^7 + 7*z^5 + 3*z^3 - 3*z^2 - 7) * q^89 + (3*z^9 + z^7 - z^6 - 3*z^4 - 6*z^2 + z - 6) * q^90 + (-5*z^9 - 3*z^7 + 3*z^6 - 3*z^5 + 3*z^4 + 5*z^2 - 3) * q^91 + (-2*z^9 - z^8 - z^7 + z^6 + 2*z^5 - z^4 + 2*z^3 + 2*z^2 - z) * q^92 + (z^9 + 5*z^6 - 5*z^5 - z^2 - 8) * q^93 + (-2*z^9 + 6*z^8 - 4*z^7 + 4*z^6 - 6*z^5 + 2*z^4 + 2*z^2 - 5*z + 2) * q^94 + (3*z^9 + 3*z^8 + 3*z^7 + 5*z^5 - z^4 + 2*z^3 - 2*z^2 + z - 5) * q^95 + (z^9 - z^6 - z^3 - z) * q^96 + (3*z^9 - 3*z^8 + 5*z^7 - 12*z^6 + 5*z^5 - 3*z^4 + 3*z^3 + 2*z - 2) * q^97 + (-4*z^7 - z^5 + 7*z^4 - 7*z^3 + z^2 + 4) * q^98 + (z^8 + z^7 + 2*z^6 - z^5 - z^4 - z^3 + 2*z^2 + z + 1) * q^99 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9}+O(q^{10})$$ 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9 $$10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9} + 4 q^{10} - 2 q^{11} - 11 q^{12} + 2 q^{13} - 15 q^{14} + 11 q^{15} - q^{16} - 9 q^{17} + 19 q^{18} + 2 q^{19} + 7 q^{20} + 33 q^{21} + 2 q^{22} + 21 q^{23} - 11 q^{25} + 9 q^{26} + 15 q^{28} - 2 q^{29} + 11 q^{31} + q^{32} - 11 q^{33} - 13 q^{34} - 17 q^{35} + 3 q^{36} - 18 q^{37} - 13 q^{38} + 4 q^{40} + 5 q^{41} - 22 q^{42} - 21 q^{43} - 2 q^{44} - 10 q^{45} - 10 q^{46} - 22 q^{47} - 11 q^{48} + 24 q^{49} - 22 q^{50} - 11 q^{51} - 20 q^{52} - 7 q^{53} + 11 q^{54} + 3 q^{55} + 7 q^{56} + 11 q^{57} + 24 q^{58} + 43 q^{59} + 11 q^{60} - 3 q^{61} + 33 q^{62} - 23 q^{63} - q^{64} + 41 q^{65} + 11 q^{66} - q^{67} + 2 q^{68} + 33 q^{69} + 6 q^{70} - 11 q^{71} + 8 q^{72} - 28 q^{73} + 18 q^{74} + 44 q^{75} + 2 q^{76} + 30 q^{77} + 34 q^{79} + 7 q^{80} + 13 q^{81} + 6 q^{82} - 3 q^{83} - 11 q^{84} + 8 q^{85} - 34 q^{86} - 33 q^{87} - 9 q^{88} - 49 q^{89} - 45 q^{90} - 52 q^{91} - q^{92} - 88 q^{93} - 11 q^{94} - 36 q^{95} + 16 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100})$$ 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9 + 4 * q^10 - 2 * q^11 - 11 * q^12 + 2 * q^13 - 15 * q^14 + 11 * q^15 - q^16 - 9 * q^17 + 19 * q^18 + 2 * q^19 + 7 * q^20 + 33 * q^21 + 2 * q^22 + 21 * q^23 - 11 * q^25 + 9 * q^26 + 15 * q^28 - 2 * q^29 + 11 * q^31 + q^32 - 11 * q^33 - 13 * q^34 - 17 * q^35 + 3 * q^36 - 18 * q^37 - 13 * q^38 + 4 * q^40 + 5 * q^41 - 22 * q^42 - 21 * q^43 - 2 * q^44 - 10 * q^45 - 10 * q^46 - 22 * q^47 - 11 * q^48 + 24 * q^49 - 22 * q^50 - 11 * q^51 - 20 * q^52 - 7 * q^53 + 11 * q^54 + 3 * q^55 + 7 * q^56 + 11 * q^57 + 24 * q^58 + 43 * q^59 + 11 * q^60 - 3 * q^61 + 33 * q^62 - 23 * q^63 - q^64 + 41 * q^65 + 11 * q^66 - q^67 + 2 * q^68 + 33 * q^69 + 6 * q^70 - 11 * q^71 + 8 * q^72 - 28 * q^73 + 18 * q^74 + 44 * q^75 + 2 * q^76 + 30 * q^77 + 34 * q^79 + 7 * q^80 + 13 * q^81 + 6 * q^82 - 3 * q^83 - 11 * q^84 + 8 * q^85 - 34 * q^86 - 33 * q^87 - 9 * q^88 - 49 * q^89 - 45 * q^90 - 52 * q^91 - q^92 - 88 * q^93 - 11 * q^94 - 36 * q^95 + 16 * q^97 + 20 * q^98 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$\chi(n)$$ $$-\zeta_{22}$$

## 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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
3.1
 0.142315 + 0.989821i 0.959493 − 0.281733i 0.654861 + 0.755750i −0.841254 − 0.540641i −0.415415 − 0.909632i −0.415415 + 0.909632i 0.142315 − 0.989821i −0.841254 + 0.540641i 0.654861 − 0.755750i 0.959493 + 0.281733i
0.142315 + 0.989821i 0.817178 1.78937i −0.959493 + 0.281733i −0.357685 + 0.412791i 1.88745 + 0.554206i −3.96028 + 2.54512i −0.415415 0.909632i −0.569485 0.657220i −0.459493 0.295298i
9.1 0.959493 0.281733i −1.80075 2.07817i 0.841254 0.540641i 0.459493 + 3.19584i −2.31329 1.48666i −0.497033 + 1.08835i 0.654861 0.755750i −0.649167 + 4.51506i 1.34125 + 2.93694i
13.1 0.654861 + 0.755750i −0.512546 0.329393i −0.142315 + 0.989821i 0.154861 0.339098i −0.0867074 0.603063i −1.97611 0.580239i −0.841254 + 0.540641i −1.09204 2.39124i 0.357685 0.105026i
25.1 −0.841254 0.540641i 0.425839 + 2.96177i 0.415415 + 0.909632i −1.34125 0.393828i 1.24302 2.72183i 2.81051 3.24350i 0.142315 0.989821i −5.71228 + 1.67728i 0.915415 + 1.05645i
27.1 −0.415415 0.909632i 1.07028 0.314261i −0.654861 + 0.755750i −0.915415 0.588302i −0.730471 0.843008i 0.122916 + 0.854902i 0.959493 + 0.281733i −1.47703 + 0.949230i −0.154861 + 1.07708i
29.1 −0.415415 + 0.909632i 1.07028 + 0.314261i −0.654861 0.755750i −0.915415 + 0.588302i −0.730471 + 0.843008i 0.122916 0.854902i 0.959493 0.281733i −1.47703 0.949230i −0.154861 1.07708i
31.1 0.142315 0.989821i 0.817178 + 1.78937i −0.959493 0.281733i −0.357685 0.412791i 1.88745 0.554206i −3.96028 2.54512i −0.415415 + 0.909632i −0.569485 + 0.657220i −0.459493 + 0.295298i
35.1 −0.841254 + 0.540641i 0.425839 2.96177i 0.415415 0.909632i −1.34125 + 0.393828i 1.24302 + 2.72183i 2.81051 + 3.24350i 0.142315 + 0.989821i −5.71228 1.67728i 0.915415 1.05645i
39.1 0.654861 0.755750i −0.512546 + 0.329393i −0.142315 0.989821i 0.154861 + 0.339098i −0.0867074 + 0.603063i −1.97611 + 0.580239i −0.841254 0.540641i −1.09204 + 2.39124i 0.357685 + 0.105026i
41.1 0.959493 + 0.281733i −1.80075 + 2.07817i 0.841254 + 0.540641i 0.459493 3.19584i −2.31329 + 1.48666i −0.497033 1.08835i 0.654861 + 0.755750i −0.649167 4.51506i 1.34125 2.93694i
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 41.1 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 46.2.c.b 10
3.b odd 2 1 414.2.i.c 10
4.b odd 2 1 368.2.m.a 10
23.c even 11 1 inner 46.2.c.b 10
23.c even 11 1 1058.2.a.j 5
23.d odd 22 1 1058.2.a.k 5
69.g even 22 1 9522.2.a.bw 5
69.h odd 22 1 414.2.i.c 10
69.h odd 22 1 9522.2.a.bz 5
92.g odd 22 1 368.2.m.a 10
92.g odd 22 1 8464.2.a.bu 5
92.h even 22 1 8464.2.a.bv 5

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
46.2.c.b 10 1.a even 1 1 trivial
46.2.c.b 10 23.c even 11 1 inner
368.2.m.a 10 4.b odd 2 1
368.2.m.a 10 92.g odd 22 1
414.2.i.c 10 3.b odd 2 1
414.2.i.c 10 69.h odd 22 1
1058.2.a.j 5 23.c even 11 1
1058.2.a.k 5 23.d odd 22 1
8464.2.a.bu 5 92.g odd 22 1
8464.2.a.bv 5 92.h even 22 1
9522.2.a.bw 5 69.g even 22 1
9522.2.a.bz 5 69.h odd 22 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{10} + 11T_{3}^{8} + 55T_{3}^{6} - 99T_{3}^{5} + 242T_{3}^{4} - 242T_{3}^{3} - 121T_{3}^{2} + 121T_{3} + 121$$ acting on $$S_{2}^{\mathrm{new}}(46, [\chi])$$.

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{10} - T^{9} + T^{8} - T^{7} + T^{6} - T^{5} + \cdots + 1$$
$3$ $$T^{10} + 11 T^{8} + 55 T^{6} + \cdots + 121$$
$5$ $$T^{10} + 4 T^{9} + 16 T^{8} + 53 T^{7} + \cdots + 1$$
$7$ $$T^{10} + 7 T^{9} + 16 T^{8} + \cdots + 1849$$
$11$ $$T^{10} + 2 T^{9} + 26 T^{8} + 74 T^{7} + \cdots + 1$$
$13$ $$T^{10} - 2 T^{9} + 48 T^{8} + \cdots + 436921$$
$17$ $$T^{10} + 9 T^{9} + 81 T^{8} + 454 T^{7} + \cdots + 1$$
$19$ $$T^{10} - 2 T^{9} + 15 T^{8} + \cdots + 139129$$
$23$ $$T^{10} - 21 T^{9} + 210 T^{8} + \cdots + 6436343$$
$29$ $$T^{10} + 2 T^{9} + 48 T^{8} - 25 T^{7} + \cdots + 529$$
$31$ $$T^{10} - 11 T^{9} + 110 T^{8} + \cdots + 2076481$$
$37$ $$T^{10} + 18 T^{9} + 225 T^{8} + \cdots + 14645929$$
$41$ $$T^{10} - 5 T^{9} + 25 T^{8} + \cdots + 1985281$$
$43$ $$T^{10} + 21 T^{9} + 232 T^{8} + \cdots + 53333809$$
$47$ $$(T^{5} + 11 T^{4} - 66 T^{3} - 726 T^{2} + \cdots + 3883)^{2}$$
$53$ $$T^{10} + 7 T^{9} + 16 T^{8} + \cdots + 1849$$
$59$ $$T^{10} - 43 T^{9} + 859 T^{8} + \cdots + 8300161$$
$61$ $$T^{10} + 3 T^{9} + 53 T^{8} + 104 T^{7} + \cdots + 529$$
$67$ $$T^{10} + T^{9} - 54 T^{8} + \cdots + 157609$$
$71$ $$T^{10} + 11 T^{9} + 110 T^{8} + \cdots + 2076481$$
$73$ $$T^{10} + 28 T^{9} + 366 T^{8} + \cdots + 34774609$$
$79$ $$T^{10} - 34 T^{9} + \cdots + 118613881$$
$83$ $$T^{10} + 3 T^{9} - 277 T^{8} + \cdots + 923126689$$
$89$ $$T^{10} + 49 T^{9} + 1191 T^{8} + \cdots + 380689$$
$97$ $$T^{10} - 16 T^{9} + \cdots + 788093329$$