# Properties

 Label 14.3.d.a Level $14$ Weight $3$ Character orbit 14.d Analytic conductor $0.381$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 14.d (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.381472370104$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\beta_2,\beta_3$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + \beta_1 q^{2} + (\beta_{3} - \beta_{2} - \beta_1 - 2) q^{3} + 2 \beta_{2} q^{4} + ( - 4 \beta_{3} + \beta_{2} - 2 \beta_1 - 1) q^{5} + ( - \beta_{3} - 4 \beta_{2} - 2 \beta_1 - 2) q^{6} + (5 \beta_{3} + 2 \beta_{2} + 4 \beta_1 + 3) q^{7} + 2 \beta_{3} q^{8} + 6 \beta_1 q^{9}+O(q^{10})$$ q + b1 * q^2 + (b3 - b2 - b1 - 2) * q^3 + 2*b2 * q^4 + (-4*b3 + b2 - 2*b1 - 1) * q^5 + (-b3 - 4*b2 - 2*b1 - 2) * q^6 + (5*b3 + 2*b2 + 4*b1 + 3) * q^7 + 2*b3 * q^8 + 6*b1 * q^9 $$q + \beta_1 q^{2} + (\beta_{3} - \beta_{2} - \beta_1 - 2) q^{3} + 2 \beta_{2} q^{4} + ( - 4 \beta_{3} + \beta_{2} - 2 \beta_1 - 1) q^{5} + ( - \beta_{3} - 4 \beta_{2} - 2 \beta_1 - 2) q^{6} + (5 \beta_{3} + 2 \beta_{2} + 4 \beta_1 + 3) q^{7} + 2 \beta_{3} q^{8} + 6 \beta_1 q^{9} + (\beta_{3} + 4 \beta_{2} - \beta_1 + 8) q^{10} + ( - 3 \beta_{3} - 9 \beta_{2} - 3 \beta_1) q^{11} + ( - 4 \beta_{3} - 2 \beta_{2} - 2 \beta_1 + 2) q^{12} + ( - 2 \beta_{3} + 12 \beta_{2} - 4 \beta_1 + 6) q^{13} + (2 \beta_{3} - 2 \beta_{2} + 3 \beta_1 - 10) q^{14} + (3 \beta_{3} - 9) q^{15} + ( - 4 \beta_{2} - 4) q^{16} + (2 \beta_{3} - 5 \beta_{2} - 2 \beta_1 - 10) q^{17} + 12 \beta_{2} q^{18} + (2 \beta_{3} - \beta_{2} + \beta_1 + 1) q^{19} + (4 \beta_{3} - 4 \beta_{2} + 8 \beta_1 - 2) q^{20} + ( - 10 \beta_{3} - 11 \beta_{2} - 8 \beta_1 + 8) q^{21} + ( - 9 \beta_{3} + 6) q^{22} + (15 \beta_{2} - 9 \beta_1 + 15) q^{23} + ( - 2 \beta_{3} + 4 \beta_{2} + 2 \beta_1 + 8) q^{24} + (12 \beta_{3} - 2 \beta_{2} + 12 \beta_1) q^{25} + (12 \beta_{3} - 4 \beta_{2} + 6 \beta_1 + 4) q^{26} + (3 \beta_{3} - 6 \beta_{2} + 6 \beta_1 - 3) q^{27} + ( - 2 \beta_{3} + 2 \beta_{2} - 10 \beta_1 - 4) q^{28} + ( - 6 \beta_{3} + 12) q^{29} + ( - 6 \beta_{2} - 9 \beta_1 - 6) q^{30} + ( - 15 \beta_{3} - 7 \beta_{2} + 15 \beta_1 - 14) q^{31} + ( - 4 \beta_{3} - 4 \beta_1) q^{32} + (24 \beta_{3} + 15 \beta_{2} + 12 \beta_1 - 15) q^{33} + ( - 5 \beta_{3} - 8 \beta_{2} - 10 \beta_1 - 4) q^{34} + ( - 14 \beta_{3} + 35 \beta_{2} - 7 \beta_1 + 7) q^{35} + 12 \beta_{3} q^{36} + ( - 31 \beta_{2} - 24 \beta_1 - 31) q^{37} + ( - \beta_{3} - 2 \beta_{2} + \beta_1 - 4) q^{38} + ( - 12 \beta_{3} - 6 \beta_{2} - 12 \beta_1) q^{39} + ( - 4 \beta_{3} + 8 \beta_{2} - 2 \beta_1 - 8) q^{40} + (10 \beta_{3} - 4 \beta_{2} + 20 \beta_1 - 2) q^{41} + ( - 11 \beta_{3} + 4 \beta_{2} + 8 \beta_1 + 20) q^{42} + ( - 6 \beta_{3} - 2) q^{43} + (18 \beta_{2} + 6 \beta_1 + 18) q^{44} + (6 \beta_{3} + 24 \beta_{2} - 6 \beta_1 + 48) q^{45} + (15 \beta_{3} - 18 \beta_{2} + 15 \beta_1) q^{46} + (2 \beta_{3} - 29 \beta_{2} + \beta_1 + 29) q^{47} + (4 \beta_{3} + 8 \beta_{2} + 8 \beta_1 + 4) q^{48} + (26 \beta_{3} - 40 \beta_{2} + 4 \beta_1 - 25) q^{49} + ( - 2 \beta_{3} - 24) q^{50} + (27 \beta_{2} + 21 \beta_1 + 27) q^{51} + ( - 4 \beta_{3} - 12 \beta_{2} + 4 \beta_1 - 24) q^{52} + ( - 12 \beta_{3} + 39 \beta_{2} - 12 \beta_1) q^{53} + ( - 6 \beta_{3} + 6 \beta_{2} - 3 \beta_1 - 6) q^{54} + ( - 15 \beta_{3} - 6 \beta_{2} - 30 \beta_1 - 3) q^{55} + (2 \beta_{3} - 16 \beta_{2} - 4 \beta_1 + 4) q^{56} + 3 q^{57} + (12 \beta_{2} + 12 \beta_1 + 12) q^{58} + (25 \beta_{3} - 13 \beta_{2} - 25 \beta_1 - 26) q^{59} + ( - 6 \beta_{3} - 18 \beta_{2} - 6 \beta_1) q^{60} + ( - 64 \beta_{3} + 7 \beta_{2} - 32 \beta_1 - 7) q^{61} + ( - 7 \beta_{3} + 60 \beta_{2} - 14 \beta_1 + 30) q^{62} + (12 \beta_{3} - 12 \beta_{2} + 18 \beta_1 - 60) q^{63} + 8 q^{64} + ( - 42 \beta_{2} + 42 \beta_1 - 42) q^{65} + (15 \beta_{3} - 24 \beta_{2} - 15 \beta_1 - 48) q^{66} + (45 \beta_{3} + 29 \beta_{2} + 45 \beta_1) q^{67} + ( - 8 \beta_{3} - 10 \beta_{2} - 4 \beta_1 + 10) q^{68} + ( - 6 \beta_{3} + 6 \beta_{2} - 12 \beta_1 + 3) q^{69} + (35 \beta_{3} + 14 \beta_{2} + 7 \beta_1 + 28) q^{70} + (30 \beta_{3} - 6) q^{71} + ( - 24 \beta_{2} - 24) q^{72} + ( - 16 \beta_{3} + 53 \beta_{2} + 16 \beta_1 + 106) q^{73} + ( - 31 \beta_{3} - 48 \beta_{2} - 31 \beta_1) q^{74} + ( - 20 \beta_{3} - 22 \beta_{2} - 10 \beta_1 + 22) q^{75} + ( - 2 \beta_{3} + 4 \beta_{2} - 4 \beta_1 + 2) q^{76} + (21 \beta_{2} + 42 \beta_1 + 42) q^{77} + ( - 6 \beta_{3} + 24) q^{78} + (55 \beta_{2} + 15 \beta_1 + 55) q^{79} + (8 \beta_{3} + 4 \beta_{2} - 8 \beta_1 + 8) q^{80} + ( - 54 \beta_{3} - 9 \beta_{2} - 54 \beta_1) q^{81} + ( - 4 \beta_{3} + 20 \beta_{2} - 2 \beta_1 - 20) q^{82} + (4 \beta_{3} - 136 \beta_{2} + 8 \beta_1 - 68) q^{83} + (4 \beta_{3} + 38 \beta_{2} + 20 \beta_1 + 22) q^{84} + (24 \beta_{3} - 9) q^{85} + (12 \beta_{2} - 2 \beta_1 + 12) q^{86} + (18 \beta_{3} - 24 \beta_{2} - 18 \beta_1 - 48) q^{87} + (18 \beta_{3} + 12 \beta_{2} + 18 \beta_1) q^{88} + (48 \beta_{3} + 63 \beta_{2} + 24 \beta_1 - 63) q^{89} + (24 \beta_{3} - 24 \beta_{2} + 48 \beta_1 - 12) q^{90} + (8 \beta_{3} + 48 \beta_{2} - 44 \beta_1 + 30) q^{91} + ( - 18 \beta_{3} - 30) q^{92} + ( - 69 \beta_{2} - 24 \beta_1 - 69) q^{93} + ( - 29 \beta_{3} - 2 \beta_{2} + 29 \beta_1 - 4) q^{94} + ( - 9 \beta_{3} + 15 \beta_{2} - 9 \beta_1) q^{95} + (8 \beta_{3} + 8 \beta_{2} + 4 \beta_1 - 8) q^{96} + ( - 26 \beta_{3} + 44 \beta_{2} - 52 \beta_1 + 22) q^{97} + ( - 40 \beta_{3} - 44 \beta_{2} - 25 \beta_1 - 52) q^{98} + ( - 54 \beta_{3} + 36) q^{99}+O(q^{100})$$ q + b1 * q^2 + (b3 - b2 - b1 - 2) * q^3 + 2*b2 * q^4 + (-4*b3 + b2 - 2*b1 - 1) * q^5 + (-b3 - 4*b2 - 2*b1 - 2) * q^6 + (5*b3 + 2*b2 + 4*b1 + 3) * q^7 + 2*b3 * q^8 + 6*b1 * q^9 + (b3 + 4*b2 - b1 + 8) * q^10 + (-3*b3 - 9*b2 - 3*b1) * q^11 + (-4*b3 - 2*b2 - 2*b1 + 2) * q^12 + (-2*b3 + 12*b2 - 4*b1 + 6) * q^13 + (2*b3 - 2*b2 + 3*b1 - 10) * q^14 + (3*b3 - 9) * q^15 + (-4*b2 - 4) * q^16 + (2*b3 - 5*b2 - 2*b1 - 10) * q^17 + 12*b2 * q^18 + (2*b3 - b2 + b1 + 1) * q^19 + (4*b3 - 4*b2 + 8*b1 - 2) * q^20 + (-10*b3 - 11*b2 - 8*b1 + 8) * q^21 + (-9*b3 + 6) * q^22 + (15*b2 - 9*b1 + 15) * q^23 + (-2*b3 + 4*b2 + 2*b1 + 8) * q^24 + (12*b3 - 2*b2 + 12*b1) * q^25 + (12*b3 - 4*b2 + 6*b1 + 4) * q^26 + (3*b3 - 6*b2 + 6*b1 - 3) * q^27 + (-2*b3 + 2*b2 - 10*b1 - 4) * q^28 + (-6*b3 + 12) * q^29 + (-6*b2 - 9*b1 - 6) * q^30 + (-15*b3 - 7*b2 + 15*b1 - 14) * q^31 + (-4*b3 - 4*b1) * q^32 + (24*b3 + 15*b2 + 12*b1 - 15) * q^33 + (-5*b3 - 8*b2 - 10*b1 - 4) * q^34 + (-14*b3 + 35*b2 - 7*b1 + 7) * q^35 + 12*b3 * q^36 + (-31*b2 - 24*b1 - 31) * q^37 + (-b3 - 2*b2 + b1 - 4) * q^38 + (-12*b3 - 6*b2 - 12*b1) * q^39 + (-4*b3 + 8*b2 - 2*b1 - 8) * q^40 + (10*b3 - 4*b2 + 20*b1 - 2) * q^41 + (-11*b3 + 4*b2 + 8*b1 + 20) * q^42 + (-6*b3 - 2) * q^43 + (18*b2 + 6*b1 + 18) * q^44 + (6*b3 + 24*b2 - 6*b1 + 48) * q^45 + (15*b3 - 18*b2 + 15*b1) * q^46 + (2*b3 - 29*b2 + b1 + 29) * q^47 + (4*b3 + 8*b2 + 8*b1 + 4) * q^48 + (26*b3 - 40*b2 + 4*b1 - 25) * q^49 + (-2*b3 - 24) * q^50 + (27*b2 + 21*b1 + 27) * q^51 + (-4*b3 - 12*b2 + 4*b1 - 24) * q^52 + (-12*b3 + 39*b2 - 12*b1) * q^53 + (-6*b3 + 6*b2 - 3*b1 - 6) * q^54 + (-15*b3 - 6*b2 - 30*b1 - 3) * q^55 + (2*b3 - 16*b2 - 4*b1 + 4) * q^56 + 3 * q^57 + (12*b2 + 12*b1 + 12) * q^58 + (25*b3 - 13*b2 - 25*b1 - 26) * q^59 + (-6*b3 - 18*b2 - 6*b1) * q^60 + (-64*b3 + 7*b2 - 32*b1 - 7) * q^61 + (-7*b3 + 60*b2 - 14*b1 + 30) * q^62 + (12*b3 - 12*b2 + 18*b1 - 60) * q^63 + 8 * q^64 + (-42*b2 + 42*b1 - 42) * q^65 + (15*b3 - 24*b2 - 15*b1 - 48) * q^66 + (45*b3 + 29*b2 + 45*b1) * q^67 + (-8*b3 - 10*b2 - 4*b1 + 10) * q^68 + (-6*b3 + 6*b2 - 12*b1 + 3) * q^69 + (35*b3 + 14*b2 + 7*b1 + 28) * q^70 + (30*b3 - 6) * q^71 + (-24*b2 - 24) * q^72 + (-16*b3 + 53*b2 + 16*b1 + 106) * q^73 + (-31*b3 - 48*b2 - 31*b1) * q^74 + (-20*b3 - 22*b2 - 10*b1 + 22) * q^75 + (-2*b3 + 4*b2 - 4*b1 + 2) * q^76 + (21*b2 + 42*b1 + 42) * q^77 + (-6*b3 + 24) * q^78 + (55*b2 + 15*b1 + 55) * q^79 + (8*b3 + 4*b2 - 8*b1 + 8) * q^80 + (-54*b3 - 9*b2 - 54*b1) * q^81 + (-4*b3 + 20*b2 - 2*b1 - 20) * q^82 + (4*b3 - 136*b2 + 8*b1 - 68) * q^83 + (4*b3 + 38*b2 + 20*b1 + 22) * q^84 + (24*b3 - 9) * q^85 + (12*b2 - 2*b1 + 12) * q^86 + (18*b3 - 24*b2 - 18*b1 - 48) * q^87 + (18*b3 + 12*b2 + 18*b1) * q^88 + (48*b3 + 63*b2 + 24*b1 - 63) * q^89 + (24*b3 - 24*b2 + 48*b1 - 12) * q^90 + (8*b3 + 48*b2 - 44*b1 + 30) * q^91 + (-18*b3 - 30) * q^92 + (-69*b2 - 24*b1 - 69) * q^93 + (-29*b3 - 2*b2 + 29*b1 - 4) * q^94 + (-9*b3 + 15*b2 - 9*b1) * q^95 + (8*b3 + 8*b2 + 4*b1 - 8) * q^96 + (-26*b3 + 44*b2 - 52*b1 + 22) * q^97 + (-40*b3 - 44*b2 - 25*b1 - 52) * q^98 + (-54*b3 + 36) * q^99 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10})$$ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 $$4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100})$$ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 + 24 * q^10 + 18 * q^11 + 12 * q^12 - 36 * q^14 - 36 * q^15 - 8 * q^16 - 30 * q^17 - 24 * q^18 + 6 * q^19 + 54 * q^21 + 24 * q^22 + 30 * q^23 + 24 * q^24 + 4 * q^25 + 24 * q^26 - 20 * q^28 + 48 * q^29 - 12 * q^30 - 42 * q^31 - 90 * q^33 - 42 * q^35 - 62 * q^37 - 12 * q^38 + 12 * q^39 - 48 * q^40 + 72 * q^42 - 8 * q^43 + 36 * q^44 + 144 * q^45 + 36 * q^46 + 174 * q^47 - 20 * q^49 - 96 * q^50 + 54 * q^51 - 72 * q^52 - 78 * q^53 - 36 * q^54 + 48 * q^56 + 12 * q^57 + 24 * q^58 - 78 * q^59 + 36 * q^60 - 42 * q^61 - 216 * q^63 + 32 * q^64 - 84 * q^65 - 144 * q^66 - 58 * q^67 + 60 * q^68 + 84 * q^70 - 24 * q^71 - 48 * q^72 + 318 * q^73 + 96 * q^74 + 132 * q^75 + 126 * q^77 + 96 * q^78 + 110 * q^79 + 24 * q^80 + 18 * q^81 - 120 * q^82 + 12 * q^84 - 36 * q^85 + 24 * q^86 - 144 * q^87 - 24 * q^88 - 378 * q^89 + 24 * q^91 - 120 * q^92 - 138 * q^93 - 12 * q^94 - 30 * q^95 - 48 * q^96 - 120 * q^98 + 144 * q^99

Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{4} + 2x^{2} + 4$$ :

 $$\beta_{1}$$ $$=$$ $$\nu$$ v $$\beta_{2}$$ $$=$$ $$( \nu^{2} ) / 2$$ (v^2) / 2 $$\beta_{3}$$ $$=$$ $$( \nu^{3} ) / 2$$ (v^3) / 2
 $$\nu$$ $$=$$ $$\beta_1$$ b1 $$\nu^{2}$$ $$=$$ $$2\beta_{2}$$ 2*b2 $$\nu^{3}$$ $$=$$ $$2\beta_{3}$$ 2*b3

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$1 + \beta_{2}$$

## 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
 −0.707107 − 1.22474i 0.707107 + 1.22474i −0.707107 + 1.22474i 0.707107 − 1.22474i
−0.707107 1.22474i 0.621320 + 0.358719i −1.00000 + 1.73205i −5.74264 + 3.31552i 1.01461i 6.24264 3.16693i 2.82843 −4.24264 7.34847i 8.12132 + 4.68885i
3.2 0.707107 + 1.22474i −3.62132 2.09077i −1.00000 + 1.73205i 2.74264 1.58346i 5.91359i −2.24264 + 6.63103i −2.82843 4.24264 + 7.34847i 3.87868 + 2.23936i
5.1 −0.707107 + 1.22474i 0.621320 0.358719i −1.00000 1.73205i −5.74264 3.31552i 1.01461i 6.24264 + 3.16693i 2.82843 −4.24264 + 7.34847i 8.12132 4.68885i
5.2 0.707107 1.22474i −3.62132 + 2.09077i −1.00000 1.73205i 2.74264 + 1.58346i 5.91359i −2.24264 6.63103i −2.82843 4.24264 7.34847i 3.87868 2.23936i
 $$n$$: 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
7.d odd 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 14.3.d.a 4
3.b odd 2 1 126.3.n.c 4
4.b odd 2 1 112.3.s.b 4
5.b even 2 1 350.3.k.a 4
5.c odd 4 2 350.3.i.a 8
7.b odd 2 1 98.3.d.a 4
7.c even 3 1 98.3.b.b 4
7.c even 3 1 98.3.d.a 4
7.d odd 6 1 inner 14.3.d.a 4
7.d odd 6 1 98.3.b.b 4
8.b even 2 1 448.3.s.d 4
8.d odd 2 1 448.3.s.c 4
12.b even 2 1 1008.3.cg.l 4
21.c even 2 1 882.3.n.b 4
21.g even 6 1 126.3.n.c 4
21.g even 6 1 882.3.c.f 4
21.h odd 6 1 882.3.c.f 4
21.h odd 6 1 882.3.n.b 4
28.d even 2 1 784.3.s.c 4
28.f even 6 1 112.3.s.b 4
28.f even 6 1 784.3.c.e 4
28.g odd 6 1 784.3.c.e 4
28.g odd 6 1 784.3.s.c 4
35.i odd 6 1 350.3.k.a 4
35.k even 12 2 350.3.i.a 8
56.j odd 6 1 448.3.s.d 4
56.m even 6 1 448.3.s.c 4
84.j odd 6 1 1008.3.cg.l 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.3.d.a 4 1.a even 1 1 trivial
14.3.d.a 4 7.d odd 6 1 inner
98.3.b.b 4 7.c even 3 1
98.3.b.b 4 7.d odd 6 1
98.3.d.a 4 7.b odd 2 1
98.3.d.a 4 7.c even 3 1
112.3.s.b 4 4.b odd 2 1
112.3.s.b 4 28.f even 6 1
126.3.n.c 4 3.b odd 2 1
126.3.n.c 4 21.g even 6 1
350.3.i.a 8 5.c odd 4 2
350.3.i.a 8 35.k even 12 2
350.3.k.a 4 5.b even 2 1
350.3.k.a 4 35.i odd 6 1
448.3.s.c 4 8.d odd 2 1
448.3.s.c 4 56.m even 6 1
448.3.s.d 4 8.b even 2 1
448.3.s.d 4 56.j odd 6 1
784.3.c.e 4 28.f even 6 1
784.3.c.e 4 28.g odd 6 1
784.3.s.c 4 28.d even 2 1
784.3.s.c 4 28.g odd 6 1
882.3.c.f 4 21.g even 6 1
882.3.c.f 4 21.h odd 6 1
882.3.n.b 4 21.c even 2 1
882.3.n.b 4 21.h odd 6 1
1008.3.cg.l 4 12.b even 2 1
1008.3.cg.l 4 84.j odd 6 1

## Hecke kernels

This newform subspace is the entire newspace $$S_{3}^{\mathrm{new}}(14, [\chi])$$.

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{4} + 2T^{2} + 4$$
$3$ $$T^{4} + 6 T^{3} + 9 T^{2} - 18 T + 9$$
$5$ $$T^{4} + 6 T^{3} - 9 T^{2} - 126 T + 441$$
$7$ $$T^{4} - 8 T^{3} + 42 T^{2} + \cdots + 2401$$
$11$ $$T^{4} - 18 T^{3} + 261 T^{2} + \cdots + 3969$$
$13$ $$T^{4} + 264T^{2} + 7056$$
$17$ $$T^{4} + 30 T^{3} + 351 T^{2} + \cdots + 2601$$
$19$ $$T^{4} - 6 T^{3} + 9 T^{2} + 18 T + 9$$
$23$ $$T^{4} - 30 T^{3} + 837 T^{2} + \cdots + 3969$$
$29$ $$(T^{2} - 24 T + 72)^{2}$$
$31$ $$T^{4} + 42 T^{3} - 615 T^{2} + \cdots + 1447209$$
$37$ $$T^{4} + 62 T^{3} + 4035 T^{2} + \cdots + 36481$$
$41$ $$T^{4} + 1224 T^{2} + 345744$$
$43$ $$(T^{2} + 4 T - 68)^{2}$$
$47$ $$T^{4} - 174 T^{3} + 12609 T^{2} + \cdots + 6335289$$
$53$ $$T^{4} + 78 T^{3} + 4851 T^{2} + \cdots + 1520289$$
$59$ $$T^{4} + 78 T^{3} - 1215 T^{2} + \cdots + 10517049$$
$61$ $$T^{4} + 42 T^{3} - 5409 T^{2} + \cdots + 35964009$$
$67$ $$T^{4} + 58 T^{3} + 6573 T^{2} + \cdots + 10297681$$
$71$ $$(T^{2} + 12 T - 1764)^{2}$$
$73$ $$T^{4} - 318 T^{3} + \cdots + 47485881$$
$79$ $$T^{4} - 110 T^{3} + 9525 T^{2} + \cdots + 6630625$$
$83$ $$T^{4} + 27936 T^{2} + \cdots + 189778176$$
$89$ $$T^{4} + 378 T^{3} + \cdots + 71419401$$
$97$ $$T^{4} + 11016 T^{2} + \cdots + 6780816$$