Properties

Label 621.2.c
Level 621621
Weight 22
Character orbit 621.c
Rep. character χ621(620,)\chi_{621}(620,\cdot)
Character field Q\Q
Dimension 3232
Newform subspaces 22
Sturm bound 144144
Trace bound 44

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Defining parameters

Level: N N == 621=3323 621 = 3^{3} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 621.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 69 69
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 144144
Trace bound: 44
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(621,[χ])M_{2}(621, [\chi]).

Total New Old
Modular forms 78 32 46
Cusp forms 66 32 34
Eisenstein series 12 0 12

Trace form

32q36q4+4q13+4q16+20q25+16q31+16q4664q4912q5236q5540q58+56q6436q7044q73+44q82+72q85+20q94+O(q100) 32 q - 36 q^{4} + 4 q^{13} + 4 q^{16} + 20 q^{25} + 16 q^{31} + 16 q^{46} - 64 q^{49} - 12 q^{52} - 36 q^{55} - 40 q^{58} + 56 q^{64} - 36 q^{70} - 44 q^{73} + 44 q^{82} + 72 q^{85} + 20 q^{94}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(621,[χ])S_{2}^{\mathrm{new}}(621, [\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}
621.2.c.a 621.c 69.c 1616 4.9594.959 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 621.2.c.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ8q2+(1+β2)q4+β12q5+q-\beta _{8}q^{2}+(-1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots
621.2.c.b 621.c 69.c 1616 4.9594.959 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 621.2.c.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+(1+β4)q4β13q5+q-\beta _{1}q^{2}+(-1+\beta _{4})q^{4}-\beta _{13}q^{5}+\cdots

Decomposition of S2old(621,[χ])S_{2}^{\mathrm{old}}(621, [\chi]) into lower level spaces

S2old(621,[χ]) S_{2}^{\mathrm{old}}(621, [\chi]) \simeq S2new(69,[χ])S_{2}^{\mathrm{new}}(69, [\chi])3^{\oplus 3}\oplusS2new(207,[χ])S_{2}^{\mathrm{new}}(207, [\chi])2^{\oplus 2}