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Properties

Label 2.16.a
Level $2$
Weight $16$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(2))\).

Total New Old
Modular forms 5 1 4
Cusp forms 3 1 2
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(1\)

Trace form

\( q - 128 q^{2} + 6252 q^{3} + 16384 q^{4} + 90510 q^{5} - 800256 q^{6} + 56 q^{7} - 2097152 q^{8} + 24738597 q^{9} + O(q^{10}) \) \( q - 128 q^{2} + 6252 q^{3} + 16384 q^{4} + 90510 q^{5} - 800256 q^{6} + 56 q^{7} - 2097152 q^{8} + 24738597 q^{9} - 11585280 q^{10} - 95889948 q^{11} + 102432768 q^{12} - 59782138 q^{13} - 7168 q^{14} + 565868520 q^{15} + 268435456 q^{16} - 1355814414 q^{17} - 3166540416 q^{18} + 3783593180 q^{19} + 1482915840 q^{20} + 350112 q^{21} + 12273913344 q^{22} - 11608845528 q^{23} - 13111394304 q^{24} - 22325518025 q^{25} + 7652113664 q^{26} + 64956341880 q^{27} + 917504 q^{28} - 28959105930 q^{29} - 72431170560 q^{30} + 253685353952 q^{31} - 34359738368 q^{32} - 599503954896 q^{33} + 173544244992 q^{34} + 5068560 q^{35} + 405317173248 q^{36} + 817641294446 q^{37} - 484299927040 q^{38} - 373757926776 q^{39} - 189813227520 q^{40} - 682333284198 q^{41} - 44814336 q^{42} + 366945604292 q^{43} - 1571060908032 q^{44} + 2239090414470 q^{45} + 1485932227584 q^{46} + 695741581776 q^{47} + 1678258470912 q^{48} - 4747561506807 q^{49} + 2857666307200 q^{50} - 8476551716328 q^{51} - 979470548992 q^{52} + 12993372468702 q^{53} - 8314411760640 q^{54} - 8678999193480 q^{55} - 117440512 q^{56} + 23655024561360 q^{57} + 3706765559040 q^{58} + 9209035340340 q^{59} + 9271189831680 q^{60} - 42338641200298 q^{61} - 32471725305856 q^{62} + 1385361432 q^{63} + 4398046511104 q^{64} - 5410881310380 q^{65} + 76736506226688 q^{66} + 30029787950636 q^{67} - 22213663358976 q^{68} - 72578502241056 q^{69} - 648775680 q^{70} + 115328696975352 q^{71} - 51880598175744 q^{72} + 43787346432122 q^{73} - 104658085689088 q^{74} - 139579138692300 q^{75} + 61990390661120 q^{76} - 5369837088 q^{77} + 47841014627328 q^{78} + 79603813043120 q^{79} + 24296093122560 q^{80} + 51135221770281 q^{81} + 87338660377344 q^{82} - 3417068864868 q^{83} + 5736235008 q^{84} - 122714762611140 q^{85} - 46969037349376 q^{86} - 181052330274360 q^{87} + 201095796228096 q^{88} - 377306179184790 q^{89} - 286603573052160 q^{90} - 3347799728 q^{91} - 190199325130752 q^{92} + 1586040832907904 q^{93} - 89054922467328 q^{94} + 342453018721800 q^{95} - 214817084276736 q^{96} - 166982186657374 q^{97} + 607687872871296 q^{98} - 2372182779922956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.16.a.a 2.a 1.a $1$ $2.854$ \(\Q\) None \(-128\) \(6252\) \(90510\) \(56\) $+$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)