# Properties

 Label 25.2.d.a Level $25$ Weight $2$ Character orbit 25.d Analytic conductor $0.200$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(6,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 25.d (of order $$5$$, degree $$4$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$0.199626005053$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ 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: $\mathrm{SU}(2)[C_{5}]$

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{10}$$. We also show the integral $$q$$-expansion of the trace form.

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

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$-\zeta_{10}^{3}$$

## 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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label   $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
6.1
 −0.309017 + 0.951057i 0.809017 + 0.587785i 0.809017 − 0.587785i −0.309017 − 0.951057i
−0.500000 1.53884i −0.809017 + 0.587785i −0.500000 + 0.363271i −0.690983 + 2.12663i 1.30902 + 0.951057i 0.618034 −1.80902 1.31433i −0.618034 + 1.90211i 3.61803
11.1 −0.500000 + 0.363271i 0.309017 0.951057i −0.500000 + 1.53884i −1.80902 1.31433i 0.190983 + 0.587785i −1.61803 −0.690983 2.12663i 1.61803 + 1.17557i 1.38197
16.1 −0.500000 0.363271i 0.309017 + 0.951057i −0.500000 1.53884i −1.80902 + 1.31433i 0.190983 0.587785i −1.61803 −0.690983 + 2.12663i 1.61803 1.17557i 1.38197
21.1 −0.500000 + 1.53884i −0.809017 0.587785i −0.500000 0.363271i −0.690983 2.12663i 1.30902 0.951057i 0.618034 −1.80902 + 1.31433i −0.618034 1.90211i 3.61803
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 25.2.d.a 4
3.b odd 2 1 225.2.h.b 4
4.b odd 2 1 400.2.u.b 4
5.b even 2 1 125.2.d.a 4
5.c odd 4 2 125.2.e.a 8
25.d even 5 1 inner 25.2.d.a 4
25.d even 5 1 625.2.a.b 2
25.d even 5 2 625.2.d.h 4
25.e even 10 1 125.2.d.a 4
25.e even 10 1 625.2.a.c 2
25.e even 10 2 625.2.d.b 4
25.f odd 20 2 125.2.e.a 8
25.f odd 20 2 625.2.b.a 4
25.f odd 20 4 625.2.e.c 8
75.h odd 10 1 5625.2.a.d 2
75.j odd 10 1 225.2.h.b 4
75.j odd 10 1 5625.2.a.f 2
100.h odd 10 1 10000.2.a.l 2
100.j odd 10 1 400.2.u.b 4
100.j odd 10 1 10000.2.a.c 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
25.2.d.a 4 1.a even 1 1 trivial
25.2.d.a 4 25.d even 5 1 inner
125.2.d.a 4 5.b even 2 1
125.2.d.a 4 25.e even 10 1
125.2.e.a 8 5.c odd 4 2
125.2.e.a 8 25.f odd 20 2
225.2.h.b 4 3.b odd 2 1
225.2.h.b 4 75.j odd 10 1
400.2.u.b 4 4.b odd 2 1
400.2.u.b 4 100.j odd 10 1
625.2.a.b 2 25.d even 5 1
625.2.a.c 2 25.e even 10 1
625.2.b.a 4 25.f odd 20 2
625.2.d.b 4 25.e even 10 2
625.2.d.h 4 25.d even 5 2
625.2.e.c 8 25.f odd 20 4
5625.2.a.d 2 75.h odd 10 1
5625.2.a.f 2 75.j odd 10 1
10000.2.a.c 2 100.j odd 10 1
10000.2.a.l 2 100.h odd 10 1

## Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(25, [\chi])$$.

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{4} + 2 T^{3} + 4 T^{2} + 3 T + 1$$
$3$ $$T^{4} + T^{3} + T^{2} + T + 1$$
$5$ $$T^{4} + 5 T^{3} + 15 T^{2} + 25 T + 25$$
$7$ $$(T^{2} + T - 1)^{2}$$
$11$ $$T^{4} + 2 T^{3} + 24 T^{2} - 32 T + 16$$
$13$ $$T^{4} - 9 T^{3} + 36 T^{2} - 54 T + 81$$
$17$ $$T^{4} - 8 T^{3} + 24 T^{2} + 8 T + 16$$
$19$ $$T^{4} + 5 T^{3} + 40 T^{2} + 50 T + 25$$
$23$ $$T^{4} + 11 T^{3} + 51 T^{2} + \cdots + 961$$
$29$ $$T^{4} - 5 T^{3} + 10 T^{2} + 25$$
$31$ $$T^{4} - 3 T^{3} + 9 T^{2} - 27 T + 81$$
$37$ $$T^{4} + 7 T^{3} + 19 T^{2} + 3 T + 1$$
$41$ $$T^{4} - 8 T^{3} + 24 T^{2} + 8 T + 16$$
$43$ $$(T^{2} + 3 T - 9)^{2}$$
$47$ $$T^{4} + 2 T^{3} + 4 T^{2} + 3 T + 1$$
$53$ $$T^{4} - 9 T^{3} + 61 T^{2} - 209 T + 361$$
$59$ $$T^{4} + 90 T^{2} - 675 T + 2025$$
$61$ $$T^{4} - 13 T^{3} + 139 T^{2} + \cdots + 1681$$
$67$ $$T^{4} + 2 T^{3} + 64 T^{2} + \cdots + 1936$$
$71$ $$T^{4} - 8 T^{3} + 34 T^{2} - 87 T + 841$$
$73$ $$T^{4} - 9 T^{3} + 81 T^{2} + \cdots + 6561$$
$79$ $$T^{4} - 15 T^{3} + 100 T^{2} + \cdots + 625$$
$83$ $$T^{4} - 9 T^{3} + 31 T^{2} + 11 T + 121$$
$89$ $$T^{4} + 20 T^{3} + 240 T^{2} + \cdots + 6400$$
$97$ $$T^{4} - 8 T^{3} + 34 T^{2} - 77 T + 121$$