↑

Properties

Label 16.8.a
Level $16$
Weight $8$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $16$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(16))\).

Total New Old
Modular forms 17 4 13
Cusp forms 11 3 8
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
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3 q + 28 q^{3} + 138 q^{5} + 664 q^{7} + 2575 q^{9} + O(q^{10}) \) \( 3 q + 28 q^{3} + 138 q^{5} + 664 q^{7} + 2575 q^{9} + 4596 q^{11} - 3278 q^{13} - 23288 q^{15} - 12714 q^{17} + 41292 q^{19} - 3360 q^{21} - 151992 q^{23} + 1349 q^{25} + 383320 q^{27} + 120066 q^{29} - 438432 q^{31} + 85904 q^{33} + 702288 q^{35} - 311254 q^{37} - 1191128 q^{39} - 167154 q^{41} + 610388 q^{43} - 78158 q^{45} - 74736 q^{47} + 267739 q^{49} - 397192 q^{51} + 615162 q^{53} + 1382872 q^{55} - 1066640 q^{57} - 777084 q^{59} + 1830562 q^{61} + 3988728 q^{63} + 3224316 q^{65} - 7499556 q^{67} - 5969248 q^{69} + 6673752 q^{71} - 6370898 q^{73} - 10287484 q^{75} + 6133152 q^{77} + 4652912 q^{79} + 7963579 q^{81} + 1276428 q^{83} - 9170060 q^{85} + 4209000 q^{87} - 6818562 q^{89} + 1169552 q^{91} + 17190784 q^{93} - 5694552 q^{95} + 13548006 q^{97} + 13726148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
16.8.a.a 16.a 1.a $1$ $4.998$ \(\Q\) None 8.8.a.b \(0\) \(-44\) \(430\) \(1224\) $+$ $\mathrm{SU}(2)$ \(q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots\)
16.8.a.b 16.a 1.a $1$ $4.998$ \(\Q\) None 2.8.a.a \(0\) \(-12\) \(-210\) \(-1016\) $-$ $\mathrm{SU}(2)$ \(q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots\)
16.8.a.c 16.a 1.a $1$ $4.998$ \(\Q\) None 8.8.a.a \(0\) \(84\) \(-82\) \(456\) $+$ $\mathrm{SU}(2)$ \(q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

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