Properties

Label 8.12.a
Level 8
Weight 12
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 8.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(8))\).

Total New Old
Modular forms 13 3 10
Cusp forms 9 3 6
Eisenstein series 4 0 4

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

\(3q \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 4378q^{5} \) \(\mathstrut +\mathstrut 35592q^{7} \) \(\mathstrut +\mathstrut 364351q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 4378q^{5} \) \(\mathstrut +\mathstrut 35592q^{7} \) \(\mathstrut +\mathstrut 364351q^{9} \) \(\mathstrut -\mathstrut 437924q^{11} \) \(\mathstrut +\mathstrut 2424354q^{13} \) \(\mathstrut -\mathstrut 10369192q^{15} \) \(\mathstrut +\mathstrut 11571734q^{17} \) \(\mathstrut -\mathstrut 29163996q^{19} \) \(\mathstrut +\mathstrut 42049248q^{21} \) \(\mathstrut +\mathstrut 3749272q^{23} \) \(\mathstrut +\mathstrut 25230069q^{25} \) \(\mathstrut +\mathstrut 67917320q^{27} \) \(\mathstrut -\mathstrut 242433102q^{29} \) \(\mathstrut +\mathstrut 297882912q^{31} \) \(\mathstrut -\mathstrut 592852720q^{33} \) \(\mathstrut +\mathstrut 101747952q^{35} \) \(\mathstrut -\mathstrut 182227398q^{37} \) \(\mathstrut +\mathstrut 826449464q^{39} \) \(\mathstrut +\mathstrut 979775598q^{41} \) \(\mathstrut -\mathstrut 1743278724q^{43} \) \(\mathstrut +\mathstrut 2138827042q^{45} \) \(\mathstrut -\mathstrut 701569872q^{47} \) \(\mathstrut +\mathstrut 2864997627q^{49} \) \(\mathstrut -\mathstrut 9990058520q^{51} \) \(\mathstrut -\mathstrut 531170102q^{53} \) \(\mathstrut +\mathstrut 10134953928q^{55} \) \(\mathstrut -\mathstrut 4445419280q^{57} \) \(\mathstrut -\mathstrut 9014835572q^{59} \) \(\mathstrut -\mathstrut 1840230702q^{61} \) \(\mathstrut +\mathstrut 36447883176q^{63} \) \(\mathstrut -\mathstrut 10820210564q^{65} \) \(\mathstrut -\mathstrut 2485905324q^{67} \) \(\mathstrut -\mathstrut 19932595552q^{69} \) \(\mathstrut +\mathstrut 30489530696q^{71} \) \(\mathstrut +\mathstrut 4016618382q^{73} \) \(\mathstrut -\mathstrut 81254774516q^{75} \) \(\mathstrut +\mathstrut 14365261728q^{77} \) \(\mathstrut +\mathstrut 47757712848q^{79} \) \(\mathstrut +\mathstrut 20946031387q^{81} \) \(\mathstrut -\mathstrut 147967912348q^{83} \) \(\mathstrut +\mathstrut 86218163220q^{85} \) \(\mathstrut +\mathstrut 47261838840q^{87} \) \(\mathstrut +\mathstrut 81753623454q^{89} \) \(\mathstrut +\mathstrut 7178123184q^{91} \) \(\mathstrut -\mathstrut 32147884160q^{93} \) \(\mathstrut -\mathstrut 11404963528q^{95} \) \(\mathstrut -\mathstrut 71551453338q^{97} \) \(\mathstrut +\mathstrut 113298667660q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(8))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
8.12.a.a \(1\) \(6.147\) \(\Q\) None \(0\) \(-36\) \(-3490\) \(-55464\) \(-\) \(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b \(2\) \(6.147\) \(\Q(\sqrt{109}) \) None \(0\) \(56\) \(7868\) \(91056\) \(+\) \(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

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