Properties

Label 273.2.bt
Level 273273
Weight 22
Character orbit 273.bt
Rep. character χ273(136,)\chi_{273}(136,\cdot)
Character field Q(ζ12)\Q(\zeta_{12})
Dimension 7676
Newform subspaces 22
Sturm bound 7474
Trace bound 11

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 273=3713 273 = 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 273.bt (of order 1212 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 91 91
Character field: Q(ζ12)\Q(\zeta_{12})
Newform subspaces: 2 2
Sturm bound: 7474
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(273,[χ])M_{2}(273, [\chi]).

Total New Old
Modular forms 164 76 88
Cusp forms 132 76 56
Eisenstein series 32 0 32

Trace form

76q+4q7+38q916q11+8q12+24q1488q1632q1912q21+8q22+36q2460q26+32q28+16q292q3140q328q352q3726q39+8q99+O(q100) 76 q + 4 q^{7} + 38 q^{9} - 16 q^{11} + 8 q^{12} + 24 q^{14} - 88 q^{16} - 32 q^{19} - 12 q^{21} + 8 q^{22} + 36 q^{24} - 60 q^{26} + 32 q^{28} + 16 q^{29} - 2 q^{31} - 40 q^{32} - 8 q^{35} - 2 q^{37} - 26 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(273,[χ])S_{2}^{\mathrm{new}}(273, [\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}
273.2.bt.a 273.bt 91.aa 3636 2.1802.180 None 273.2.bt.a 00 00 00 66 SU(2)[C12]\mathrm{SU}(2)[C_{12}]
273.2.bt.b 273.bt 91.aa 4040 2.1802.180 None 273.2.bt.b 00 00 00 2-2 SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Decomposition of S2old(273,[χ])S_{2}^{\mathrm{old}}(273, [\chi]) into lower level spaces

S2old(273,[χ]) S_{2}^{\mathrm{old}}(273, [\chi]) \simeq S2new(91,[χ])S_{2}^{\mathrm{new}}(91, [\chi])2^{\oplus 2}