Properties

Label 16.12.a
Level 16
Weight 12
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 24
Trace bound 3

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(16))\).

Total New Old
Modular forms 25 6 19
Cusp forms 19 5 14
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.
\(+\)\(3\)
\(-\)\(2\)

Trace form

\( 5q + 244q^{3} - 1322q^{5} - 68152q^{7} + 339817q^{9} + O(q^{10}) \) \( 5q + 244q^{3} - 1322q^{5} - 68152q^{7} + 339817q^{9} + 212732q^{11} + 123022q^{13} + 3718552q^{15} + 2386298q^{17} + 13952132q^{19} + 12388896q^{21} - 15109672q^{23} + 61783619q^{25} - 40065848q^{27} - 183066498q^{29} - 103299040q^{31} - 298469776q^{33} + 498296688q^{35} + 346926262q^{37} - 1570233992q^{39} + 62633826q^{41} + 1794010652q^{43} + 651613582q^{45} - 2108993232q^{47} + 1621590093q^{49} + 10554130856q^{51} - 1021104218q^{53} - 15975322488q^{55} - 4106770544q^{57} + 23266819244q^{59} + 1262097502q^{61} - 42744151704q^{63} + 4538759716q^{65} + 33281496884q^{67} - 11476529056q^{69} - 60900642296q^{71} + 3416691010q^{73} + 119699811116q^{75} - 9841925280q^{77} - 99564430000q^{79} - 16614818003q^{81} + 111732583108q^{83} + 76865658060q^{85} - 115244963016q^{87} + 27045197490q^{89} + 68128310320q^{91} + 27673840768q^{93} + 7826480248q^{95} - 19977510998q^{97} - 24971649364q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(16))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.12.a.a \(1\) \(12.293\) \(\Q\) None \(0\) \(-252\) \(4830\) \(16744\) \(-\) \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b \(1\) \(12.293\) \(\Q\) None \(0\) \(36\) \(-3490\) \(55464\) \(+\) \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c \(1\) \(12.293\) \(\Q\) None \(0\) \(516\) \(-10530\) \(-49304\) \(-\) \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
16.12.a.d \(2\) \(12.293\) \(\Q(\sqrt{109}) \) None \(0\) \(-56\) \(7868\) \(-91056\) \(+\) \(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)