Properties

Label 16.20.a
Level $16$
Weight $20$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $6$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(16))\).

Total New Old
Modular forms 41 10 31
Cusp forms 35 9 26
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
\(+\)\(5\)
\(-\)\(4\)

Trace form

\( 9 q + 19684 q^{3} + 1782958 q^{5} - 143716952 q^{7} + 2289890269 q^{9} + O(q^{10}) \) \( 9 q + 19684 q^{3} + 1782958 q^{5} - 143716952 q^{7} + 2289890269 q^{9} + 1373123276 q^{11} - 18820611578 q^{13} - 246226810568 q^{15} + 329867871938 q^{17} + 705960138804 q^{19} + 1651988169888 q^{21} - 15628077098632 q^{23} + 43266691637759 q^{25} - 26044795158488 q^{27} - 38532983360202 q^{29} + 229278333745056 q^{31} - 43654297068496 q^{33} + 26752252007088 q^{35} + 102642952528142 q^{37} + 1710873898963096 q^{39} + 445210909184394 q^{41} + 5147709877639532 q^{43} + 7807452800582662 q^{45} - 3863206886047632 q^{47} + 15319387730507185 q^{49} - 8418326437013368 q^{51} - 2983322710140098 q^{53} + 43021424685701992 q^{55} + 79399431180980176 q^{57} + 43714416379844540 q^{59} - 151355200634887274 q^{61} - 41710513679162424 q^{63} - 263302524614118284 q^{65} + 170129195724753444 q^{67} + 155481401778122720 q^{69} - 634507926290147096 q^{71} + 374937243811331050 q^{73} - 1386657165795430084 q^{75} - 837760884340933920 q^{77} + 758814575996517392 q^{79} - 947243107680876143 q^{81} + 718392409801962868 q^{83} + 1138692372257275900 q^{85} - 1413786216188272296 q^{87} + 2245489605574805658 q^{89} + 5742632485531790960 q^{91} - 3775942086628026752 q^{93} - 498099791399432552 q^{95} - 5149037263651067598 q^{97} + 18104119627008711740 q^{99} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.20.a.a 16.a 1.a $1$ $36.611$ \(\Q\) None \(0\) \(-50652\) \(-2377410\) \(16917544\) $-$ $\mathrm{SU}(2)$ \(q-50652q^{3}-2377410q^{5}+16917544q^{7}+\cdots\)
16.20.a.b 16.a 1.a $1$ $36.611$ \(\Q\) None \(0\) \(36\) \(-196290\) \(35905576\) $-$ $\mathrm{SU}(2)$ \(q+6^{2}q^{3}-196290q^{5}+35905576q^{7}+\cdots\)
16.20.a.c 16.a 1.a $1$ $36.611$ \(\Q\) None \(0\) \(13092\) \(6546750\) \(-96674264\) $-$ $\mathrm{SU}(2)$ \(q+13092q^{3}+6546750q^{5}-96674264q^{7}+\cdots\)
16.20.a.d 16.a 1.a $1$ $36.611$ \(\Q\) None \(0\) \(53028\) \(-5556930\) \(44496424\) $-$ $\mathrm{SU}(2)$ \(q+53028q^{3}-5556930q^{5}+44496424q^{7}+\cdots\)
16.20.a.e 16.a 1.a $2$ $36.611$ \(\Q(\sqrt{1453}) \) None \(0\) \(27912\) \(1226620\) \(-88510512\) $+$ $\mathrm{SU}(2)$ \(q+(13956-\beta )q^{3}+(613310-44\beta )q^{5}+\cdots\)
16.20.a.f 16.a 1.a $3$ $36.611$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-23732\) \(2140218\) \(-55851720\) $+$ $\mathrm{SU}(2)$ \(q+(-7911+\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)