Properties

Label 2028.2.q
Level 20282028
Weight 22
Character orbit 2028.q
Rep. character χ2028(361,)\chi_{2028}(361,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 5050
Newform subspaces 1010
Sturm bound 728728
Trace bound 1717

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Defining parameters

Level: N N == 2028=223132 2028 = 2^{2} \cdot 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2028.q (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 13 13
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 10 10
Sturm bound: 728728
Trace bound: 1717
Distinguishing TpT_p: 55, 77, 1111

Dimensions

The following table gives the dimensions of various subspaces of M2(2028,[χ])M_{2}(2028, [\chi]).

Total New Old
Modular forms 812 50 762
Cusp forms 644 50 594
Eisenstein series 168 0 168

Trace form

50q+q33q725q918q116q15+6q17+18q192q2326q252q27+4q29+6q33+18q356q37+6q4115q43+14q49+16q51+39q97+O(q100) 50 q + q^{3} - 3 q^{7} - 25 q^{9} - 18 q^{11} - 6 q^{15} + 6 q^{17} + 18 q^{19} - 2 q^{23} - 26 q^{25} - 2 q^{27} + 4 q^{29} + 6 q^{33} + 18 q^{35} - 6 q^{37} + 6 q^{41} - 15 q^{43} + 14 q^{49} + 16 q^{51}+ \cdots - 39 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(2028,[χ])S_{2}^{\mathrm{new}}(2028, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
2028.2.q.a 2028.q 13.e 22 16.19416.194 Q(3)\Q(\sqrt{-3}) None 156.2.q.a 00 11 00 6-6 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1ζ6)q3+(12ζ6)q5+(4+2ζ6)q7+q+(1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots
2028.2.q.b 2028.q 13.e 22 16.19416.194 Q(3)\Q(\sqrt{-3}) None 156.2.b.a 00 11 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1ζ6)q3+(2+4ζ6)q5ζ6q9+q+(1-\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots
2028.2.q.c 2028.q 13.e 22 16.19416.194 Q(3)\Q(\sqrt{-3}) None 156.2.b.a 00 11 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1ζ6)q3+(24ζ6)q5ζ6q9+q+(1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots
2028.2.q.d 2028.q 13.e 44 16.19416.194 Q(ζ12)\Q(\zeta_{12}) None 156.2.a.b 00 2-2 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ2q3β1q7+(β21)q9+q-\beta_{2} q^{3}-\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots
2028.2.q.e 2028.q 13.e 44 16.19416.194 Q(ζ12)\Q(\zeta_{12}) None 156.2.b.b 00 2-2 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ2q3+β3q52β1q7+(β21)q9+q-\beta_{2} q^{3}+\beta_{3} q^{5}-2\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots
2028.2.q.f 2028.q 13.e 44 16.19416.194 Q(3,43)\Q(\sqrt{-3}, \sqrt{-43}) None 156.2.q.b 00 2-2 00 33 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ2q3+(β1β2β3)q5+(β1+β2+)q7+q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots
2028.2.q.g 2028.q 13.e 44 16.19416.194 Q(ζ12)\Q(\zeta_{12}) None 156.2.i.a 00 22 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+ζ122q3+2ζ123q5+ζ12q7+q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots
2028.2.q.h 2028.q 13.e 44 16.19416.194 Q(ζ12)\Q(\zeta_{12}) None 156.2.a.a 00 22 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β2q3+2β3q5+β1q7+(β21)q9+q+\beta_{2} q^{3}+2\beta_{3} q^{5}+\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots
2028.2.q.i 2028.q 13.e 1212 16.19416.194 12.0.\cdots.1 None 2028.2.a.k 00 6-6 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1+β7)q3+(2β2+β6β8+)q5+q+(-1+\beta _{7})q^{3}+(-2\beta _{2}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots
2028.2.q.j 2028.q 13.e 1212 16.19416.194 12.0.\cdots.1 None 2028.2.a.i 00 66 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β7q3+(β2β8β11)q5+(β1+)q7+q+\beta _{7}q^{3}+(-\beta _{2}-\beta _{8}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots

Decomposition of S2old(2028,[χ])S_{2}^{\mathrm{old}}(2028, [\chi]) into lower level spaces