Properties

Label 1764.2.bm
Level 17641764
Weight 22
Character orbit 1764.bm
Rep. character χ1764(1685,)\chi_{1764}(1685,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 8080
Newform subspaces 33
Sturm bound 672672
Trace bound 99

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Defining parameters

Level: N N == 1764=223272 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1764.bm (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 63 63
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 3 3
Sturm bound: 672672
Trace bound: 99
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(1764,[χ])M_{2}(1764, [\chi]).

Total New Old
Modular forms 720 80 640
Cusp forms 624 80 544
Eisenstein series 96 0 96

Trace form

80q2q93q13+9q15+9q17+80q25+9q276q296q31+27q33q37q396q41+2q43+15q45+18q4727q51+12q5311q57++41q99+O(q100) 80 q - 2 q^{9} - 3 q^{13} + 9 q^{15} + 9 q^{17} + 80 q^{25} + 9 q^{27} - 6 q^{29} - 6 q^{31} + 27 q^{33} - q^{37} - q^{39} - 6 q^{41} + 2 q^{43} + 15 q^{45} + 18 q^{47} - 27 q^{51} + 12 q^{53} - 11 q^{57}+ \cdots + 41 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1764,[χ])S_{2}^{\mathrm{new}}(1764, [\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}
1764.2.bm.a 1764.bm 63.s 1616 14.08614.086 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 252.2.w.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(β3β12)q3+(β7β9)q5+(β5+)q9+q+(-\beta _{3}-\beta _{12})q^{3}+(\beta _{7}-\beta _{9})q^{5}+(-\beta _{5}+\cdots)q^{9}+\cdots
1764.2.bm.b 1764.bm 63.s 1616 14.08614.086 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 252.2.x.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β1q3+β15q5+β2q9+(β2+)q11+q+\beta _{1}q^{3}+\beta _{15}q^{5}+\beta _{2}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots
1764.2.bm.c 1764.bm 63.s 4848 14.08614.086 None 1764.2.x.c 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S2old(1764,[χ])S_{2}^{\mathrm{old}}(1764, [\chi]) into lower level spaces

S2old(1764,[χ]) S_{2}^{\mathrm{old}}(1764, [\chi]) \simeq S2new(63,[χ])S_{2}^{\mathrm{new}}(63, [\chi])6^{\oplus 6}\oplusS2new(126,[χ])S_{2}^{\mathrm{new}}(126, [\chi])4^{\oplus 4}\oplusS2new(252,[χ])S_{2}^{\mathrm{new}}(252, [\chi])2^{\oplus 2}\oplusS2new(441,[χ])S_{2}^{\mathrm{new}}(441, [\chi])3^{\oplus 3}\oplusS2new(882,[χ])S_{2}^{\mathrm{new}}(882, [\chi])2^{\oplus 2}