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Properties

Label 16.24.a
Level $16$
Weight $24$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(16))\).

Total New Old
Modular forms 49 12 37
Cusp forms 43 11 32
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
\(+\)\(6\)
\(-\)\(5\)

Trace form

\( 11 q + 177148 q^{3} + 17776698 q^{5} + 1949733464 q^{7} + 311299352311 q^{9} + O(q^{10}) \) \( 11 q + 177148 q^{3} + 17776698 q^{5} + 1949733464 q^{7} + 311299352311 q^{9} + 1343722145172 q^{11} + 2642407039522 q^{13} + 43176794598472 q^{15} - 71179668690714 q^{17} + 350914123605164 q^{19} - 488799515306016 q^{21} - 5818970285179512 q^{23} + 20411609150781629 q^{25} + 67444250293958680 q^{27} - 30180920062932366 q^{29} - 332360507768017312 q^{31} - 437922770794372336 q^{33} + 481627892954267088 q^{35} + 1337878249433658586 q^{37} + 2103652896914624872 q^{39} + 2097811779257112414 q^{41} - 10619192448946474252 q^{43} - 5312701887192315998 q^{45} + 29505682426017569424 q^{47} + 9145321554560946339 q^{49} + 40292411774673729080 q^{51} + 48199073743456642602 q^{53} - 131177525254463064168 q^{55} + 105086166253981385200 q^{57} + 296847161077862393508 q^{59} + 104721834516986960146 q^{61} + 605325286716663206328 q^{63} + 700960527765839036316 q^{65} + 532052647488102437564 q^{67} + 1011507184228456053152 q^{69} + 3117697388767923831576 q^{71} + 2873112734549390847742 q^{73} - 4292498618338767425884 q^{75} - 2473386093596481891168 q^{77} - 3350594355482510156560 q^{79} - 2160224273272199335805 q^{81} + 28200411317911679773548 q^{83} + 9291708797924172337620 q^{85} - 14060896771764706007640 q^{87} + 25770260157052733876430 q^{89} - 28690799643126852649712 q^{91} - 102449620519375211977856 q^{93} - 40691226128226209968152 q^{95} - 52068968829279618175754 q^{97} - 158766752571676341145372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.24.a.a 16.a 1.a $1$ $53.633$ \(\Q\) None \(0\) \(505908\) \(-90135570\) \(-6872255096\) $-$ $\mathrm{SU}(2)$ \(q+505908q^{3}-90135570q^{5}-6872255096q^{7}+\cdots\)
16.24.a.b 16.a 1.a $2$ $53.633$ \(\Q(\sqrt{144169}) \) None \(0\) \(-339480\) \(73069020\) \(1359184400\) $-$ $\mathrm{SU}(2)$ \(q+(-169740-3\beta )q^{3}+(36534510+\cdots)q^{5}+\cdots\)
16.24.a.c 16.a 1.a $2$ $53.633$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-170520\) \(-92266020\) \(-192083440\) $-$ $\mathrm{SU}(2)$ \(q+(-85260-\beta )q^{3}+(-46133010+\cdots)q^{5}+\cdots\)
16.24.a.d 16.a 1.a $3$ $53.633$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-32708\) \(31480650\) \(-993025320\) $+$ $\mathrm{SU}(2)$ \(q+(-10903-\beta _{1})q^{3}+(10493544+\cdots)q^{5}+\cdots\)
16.24.a.e 16.a 1.a $3$ $53.633$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(213948\) \(95628618\) \(8647912920\) $+$ $\mathrm{SU}(2)$ \(q+(71316+\beta _{1})q^{3}+(31876206+29\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)