Properties

Label 644.1.h
Level 644644
Weight 11
Character orbit 644.h
Rep. character χ644(643,)\chi_{644}(643,\cdot)
Character field Q\Q
Dimension 66
Newform subspaces 44
Sturm bound 9696
Trace bound 77

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Defining parameters

Level: N N == 644=22723 644 = 2^{2} \cdot 7 \cdot 23
Weight: k k == 1 1
Character orbit: [χ][\chi] == 644.h (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 644 644
Character field: Q\Q
Newform subspaces: 4 4
Sturm bound: 9696
Trace bound: 77

Dimensions

The following table gives the dimensions of various subspaces of M1(644,[χ])M_{1}(644, [\chi]).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

DnD_n A4A_4 S4S_4 A5A_5
Dimension 6 0 0 0

Trace form

6q2q2+6q42q8+2q9+6q166q18+2q254q292q32+2q36+6q496q504q58+6q646q724q772q818q858q93+2q98+O(q100) 6 q - 2 q^{2} + 6 q^{4} - 2 q^{8} + 2 q^{9} + 6 q^{16} - 6 q^{18} + 2 q^{25} - 4 q^{29} - 2 q^{32} + 2 q^{36} + 6 q^{49} - 6 q^{50} - 4 q^{58} + 6 q^{64} - 6 q^{72} - 4 q^{77} - 2 q^{81} - 8 q^{85} - 8 q^{93}+ \cdots - 2 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(644,[χ])S_{1}^{\mathrm{new}}(644, [\chi]) into newform subspaces

Label Char Prim Dim AA Field Image CM RM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
644.1.h.a 644.h 644.h 11 0.3210.321 Q\Q D2D_{2} Q(7)\Q(\sqrt{-7}) , Q(161)\Q(\sqrt{-161}) Q(23)\Q(\sqrt{23}) 644.1.h.a 11 00 00 1-1 q+q2+q4q7+q8q9+2q11+q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}+2q^{11}+\cdots
644.1.h.b 644.h 644.h 11 0.3210.321 Q\Q D2D_{2} Q(7)\Q(\sqrt{-7}) , Q(161)\Q(\sqrt{-161}) Q(23)\Q(\sqrt{23}) 644.1.h.a 11 00 00 11 q+q2+q4+q7+q8q92q11+q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}-2q^{11}+\cdots
644.1.h.c 644.h 644.h 22 0.3210.321 Q(2)\Q(\sqrt{2}) D4D_{4} Q(161)\Q(\sqrt{-161}) None 644.1.h.c 2-2 00 00 2-2 qq2βq3+q4βq5+βq6q7+q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots
644.1.h.d 644.h 644.h 22 0.3210.321 Q(2)\Q(\sqrt{2}) D4D_{4} Q(161)\Q(\sqrt{-161}) None 644.1.h.c 2-2 00 00 22 qq2+βq3+q4βq5βq6+q7+q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots