Properties

Label 12.10.a
Level 12
Weight 10
Character orbit a
Rep. character \(\chi_{12}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 12.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(12))\).

Total New Old
Modular forms 21 1 20
Cusp forms 15 1 14
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut +\mathstrut 990q^{5} \) \(\mathstrut +\mathstrut 8576q^{7} \) \(\mathstrut +\mathstrut 6561q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut +\mathstrut 990q^{5} \) \(\mathstrut +\mathstrut 8576q^{7} \) \(\mathstrut +\mathstrut 6561q^{9} \) \(\mathstrut +\mathstrut 70596q^{11} \) \(\mathstrut -\mathstrut 2530q^{13} \) \(\mathstrut -\mathstrut 80190q^{15} \) \(\mathstrut -\mathstrut 200574q^{17} \) \(\mathstrut -\mathstrut 695620q^{19} \) \(\mathstrut -\mathstrut 694656q^{21} \) \(\mathstrut +\mathstrut 2472696q^{23} \) \(\mathstrut -\mathstrut 973025q^{25} \) \(\mathstrut -\mathstrut 531441q^{27} \) \(\mathstrut +\mathstrut 5474214q^{29} \) \(\mathstrut +\mathstrut 3732104q^{31} \) \(\mathstrut -\mathstrut 5718276q^{33} \) \(\mathstrut +\mathstrut 8490240q^{35} \) \(\mathstrut -\mathstrut 21898522q^{37} \) \(\mathstrut +\mathstrut 204930q^{39} \) \(\mathstrut -\mathstrut 23818950q^{41} \) \(\mathstrut +\mathstrut 10612676q^{43} \) \(\mathstrut +\mathstrut 6495390q^{45} \) \(\mathstrut +\mathstrut 2398464q^{47} \) \(\mathstrut +\mathstrut 33194169q^{49} \) \(\mathstrut +\mathstrut 16246494q^{51} \) \(\mathstrut -\mathstrut 8994978q^{53} \) \(\mathstrut +\mathstrut 69890040q^{55} \) \(\mathstrut +\mathstrut 56345220q^{57} \) \(\mathstrut -\mathstrut 143417916q^{59} \) \(\mathstrut -\mathstrut 19804258q^{61} \) \(\mathstrut +\mathstrut 56267136q^{63} \) \(\mathstrut -\mathstrut 2504700q^{65} \) \(\mathstrut -\mathstrut 165625156q^{67} \) \(\mathstrut -\mathstrut 200288376q^{69} \) \(\mathstrut -\mathstrut 194801400q^{71} \) \(\mathstrut +\mathstrut 148729418q^{73} \) \(\mathstrut +\mathstrut 78815025q^{75} \) \(\mathstrut +\mathstrut 605431296q^{77} \) \(\mathstrut -\mathstrut 30134152q^{79} \) \(\mathstrut +\mathstrut 43046721q^{81} \) \(\mathstrut +\mathstrut 302054076q^{83} \) \(\mathstrut -\mathstrut 198568260q^{85} \) \(\mathstrut -\mathstrut 443411334q^{87} \) \(\mathstrut +\mathstrut 909502650q^{89} \) \(\mathstrut -\mathstrut 21697280q^{91} \) \(\mathstrut -\mathstrut 302300424q^{93} \) \(\mathstrut -\mathstrut 688663800q^{95} \) \(\mathstrut -\mathstrut 872463358q^{97} \) \(\mathstrut +\mathstrut 463180356q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(12))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
12.10.a.a \(1\) \(6.180\) \(\Q\) None \(0\) \(-81\) \(990\) \(8576\) \(-\) \(+\) \(q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)