Properties

Label 414.2.e
Level 414414
Weight 22
Character orbit 414.e
Rep. character χ414(139,)\chi_{414}(139,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 4444
Newform subspaces 55
Sturm bound 144144
Trace bound 55

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Defining parameters

Level: N N == 414=23223 414 = 2 \cdot 3^{2} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 414.e (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 9 9
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 5 5
Sturm bound: 144144
Trace bound: 55
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(414,[χ])M_{2}(414, [\chi]).

Total New Old
Modular forms 152 44 108
Cusp forms 136 44 92
Eisenstein series 16 0 16

Trace form

44q+2q2+2q322q4+2q6+4q74q814q910q114q12+4q13+20q1522q16+28q174q18+4q1916q216q22+2q24++12q99+O(q100) 44 q + 2 q^{2} + 2 q^{3} - 22 q^{4} + 2 q^{6} + 4 q^{7} - 4 q^{8} - 14 q^{9} - 10 q^{11} - 4 q^{12} + 4 q^{13} + 20 q^{15} - 22 q^{16} + 28 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 6 q^{22} + 2 q^{24}+ \cdots + 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(414,[χ])S_{2}^{\mathrm{new}}(414, [\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}
414.2.e.a 414.e 9.c 22 3.3063.306 Q(3)\Q(\sqrt{-3}) None 414.2.e.a 11 33 4-4 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1ζ6)q2+(1+ζ6)q3ζ6q4+q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots
414.2.e.b 414.e 9.c 1010 3.3063.306 10.0.\cdots.1 None 414.2.e.b 5-5 11 5-5 3-3 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ3q2β7q3+(1+β3)q4+(1+)q5+q-\beta _{3}q^{2}-\beta _{7}q^{3}+(-1+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots
414.2.e.c 414.e 9.c 1010 3.3063.306 10.0.\cdots.1 None 414.2.e.c 5-5 11 55 55 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1β4)q2+(1+β5β6β9)q3+q+(-1-\beta _{4})q^{2}+(1+\beta _{5}-\beta _{6}-\beta _{9})q^{3}+\cdots
414.2.e.d 414.e 9.c 1010 3.3063.306 10.0.\cdots.1 None 414.2.e.d 55 3-3 1-1 55 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β7)q2+β1q3+β7q4+(β2+)q5+q+(1+\beta _{7})q^{2}+\beta _{1}q^{3}+\beta _{7}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots
414.2.e.e 414.e 9.c 1212 3.3063.306 Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots) None 414.2.e.e 66 00 55 3-3 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β2q2β1q3+(1+β2)q4+(1+)q5+q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots

Decomposition of S2old(414,[χ])S_{2}^{\mathrm{old}}(414, [\chi]) into lower level spaces

S2old(414,[χ]) S_{2}^{\mathrm{old}}(414, [\chi]) \simeq S2new(18,[χ])S_{2}^{\mathrm{new}}(18, [\chi])2^{\oplus 2}\oplusS2new(207,[χ])S_{2}^{\mathrm{new}}(207, [\chi])2^{\oplus 2}