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

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

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

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