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Properties

Label 16.10.a
Level $16$
Weight $10$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $20$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(20\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(16))\).

Total New Old
Modular forms 21 5 16
Cusp forms 15 4 11
Eisenstein series 6 1 5

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
\(+\)\(2\)
\(-\)\(2\)

Trace form

\( 4 q - 80 q^{3} - 360 q^{5} + 1376 q^{7} + 5812 q^{9} + O(q^{10}) \) \( 4 q - 80 q^{3} - 360 q^{5} + 1376 q^{7} + 5812 q^{9} - 10992 q^{11} - 43080 q^{13} + 60448 q^{15} + 172104 q^{17} - 296336 q^{19} - 336768 q^{21} + 1349664 q^{23} - 30468 q^{25} - 5005088 q^{27} + 1723896 q^{29} + 13751680 q^{31} - 3529024 q^{33} - 27870144 q^{35} + 1408792 q^{37} + 46429600 q^{39} + 4797864 q^{41} - 78798192 q^{43} - 6847304 q^{45} + 139372608 q^{47} + 3427300 q^{49} - 202646944 q^{51} - 10028712 q^{53} + 216893536 q^{55} + 25903936 q^{57} - 224197296 q^{59} - 10080648 q^{61} + 293290464 q^{63} - 64788144 q^{65} - 255761744 q^{67} + 121435520 q^{69} - 39174048 q^{71} - 15735768 q^{73} + 276237392 q^{75} - 120707712 q^{77} - 341312064 q^{79} - 113638172 q^{81} + 758656368 q^{83} + 277817008 q^{85} - 1417283424 q^{87} + 573376104 q^{89} + 1721466688 q^{91} - 1004178944 q^{93} - 2153970528 q^{95} - 728181880 q^{97} + 2808900560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.10.a.a 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(-228\) \(-666\) \(6328\) $-$ $\mathrm{SU}(2)$ \(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(-68\) \(1510\) \(-10248\) $+$ $\mathrm{SU}(2)$ \(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(60\) \(-2074\) \(4344\) $+$ $\mathrm{SU}(2)$ \(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(156\) \(870\) \(952\) $-$ $\mathrm{SU}(2)$ \(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)