Properties

Label 1596.2.u
Level 15961596
Weight 22
Character orbit 1596.u
Rep. character χ1596(145,)\chi_{1596}(145,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 5252
Newform subspaces 33
Sturm bound 640640
Trace bound 11

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Defining parameters

Level: N N == 1596=223719 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1596.u (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 133 133
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 3 3
Sturm bound: 640640
Trace bound: 11
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(1596,[χ])M_{2}(1596, [\chi]).

Total New Old
Modular forms 664 52 612
Cusp forms 616 52 564
Eisenstein series 48 0 48

Trace form

52q+q726q96q113q1312q179q19+3q2164q25+3q31+16q353q373q3912q41+13q436q456q4725q49+12q55+6q99+O(q100) 52 q + q^{7} - 26 q^{9} - 6 q^{11} - 3 q^{13} - 12 q^{17} - 9 q^{19} + 3 q^{21} - 64 q^{25} + 3 q^{31} + 16 q^{35} - 3 q^{37} - 3 q^{39} - 12 q^{41} + 13 q^{43} - 6 q^{45} - 6 q^{47} - 25 q^{49} + 12 q^{55}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1596,[χ])S_{2}^{\mathrm{new}}(1596, [\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}
1596.2.u.a 1596.u 133.i 22 12.74412.744 Q(3)\Q(\sqrt{-3}) None 1596.2.u.a 00 1-1 00 4-4 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qζ6q3+(1+2ζ6)q5+(12ζ6)q7+q-\zeta_{6}q^{3}+(-1+2\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots
1596.2.u.b 1596.u 133.i 2424 12.74412.744 None 1596.2.u.b 00 12-12 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
1596.2.u.c 1596.u 133.i 2626 12.74412.744 None 1596.2.u.c 00 1313 00 55 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S2old(1596,[χ])S_{2}^{\mathrm{old}}(1596, [\chi]) into lower level spaces

S2old(1596,[χ]) S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq S2new(133,[χ])S_{2}^{\mathrm{new}}(133, [\chi])6^{\oplus 6}\oplusS2new(266,[χ])S_{2}^{\mathrm{new}}(266, [\chi])4^{\oplus 4}\oplusS2new(399,[χ])S_{2}^{\mathrm{new}}(399, [\chi])3^{\oplus 3}\oplusS2new(532,[χ])S_{2}^{\mathrm{new}}(532, [\chi])2^{\oplus 2}\oplusS2new(798,[χ])S_{2}^{\mathrm{new}}(798, [\chi])2^{\oplus 2}