Properties

Label 12.12.a
Level 12
Weight 12
Character orbit a
Rep. character \(\chi_{12}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 24
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 12.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 25 2 23
Cusp forms 19 2 17
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.
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\(2q \) \(\mathstrut +\mathstrut 12852q^{5} \) \(\mathstrut -\mathstrut 77000q^{7} \) \(\mathstrut +\mathstrut 118098q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 12852q^{5} \) \(\mathstrut -\mathstrut 77000q^{7} \) \(\mathstrut +\mathstrut 118098q^{9} \) \(\mathstrut -\mathstrut 137808q^{11} \) \(\mathstrut +\mathstrut 1092700q^{13} \) \(\mathstrut -\mathstrut 1732104q^{15} \) \(\mathstrut -\mathstrut 2702700q^{17} \) \(\mathstrut +\mathstrut 170800q^{19} \) \(\mathstrut +\mathstrut 23147208q^{21} \) \(\mathstrut -\mathstrut 25261200q^{23} \) \(\mathstrut +\mathstrut 10334894q^{25} \) \(\mathstrut -\mathstrut 226450188q^{29} \) \(\mathstrut +\mathstrut 374152408q^{31} \) \(\mathstrut +\mathstrut 358230600q^{33} \) \(\mathstrut -\mathstrut 834294384q^{35} \) \(\mathstrut -\mathstrut 135236900q^{37} \) \(\mathstrut +\mathstrut 732207600q^{39} \) \(\mathstrut -\mathstrut 1031482620q^{41} \) \(\mathstrut +\mathstrut 1563677200q^{43} \) \(\mathstrut +\mathstrut 758897748q^{45} \) \(\mathstrut -\mathstrut 4139780400q^{47} \) \(\mathstrut +\mathstrut 3546699282q^{49} \) \(\mathstrut +\mathstrut 1436386608q^{51} \) \(\mathstrut -\mathstrut 2251057500q^{53} \) \(\mathstrut -\mathstrut 6139603008q^{55} \) \(\mathstrut -\mathstrut 153527400q^{57} \) \(\mathstrut +\mathstrut 14284492992q^{59} \) \(\mathstrut -\mathstrut 700025396q^{61} \) \(\mathstrut -\mathstrut 4546773000q^{63} \) \(\mathstrut -\mathstrut 3717354600q^{65} \) \(\mathstrut -\mathstrut 1966587200q^{67} \) \(\mathstrut -\mathstrut 14765714208q^{69} \) \(\mathstrut +\mathstrut 25293783600q^{71} \) \(\mathstrut -\mathstrut 13777935500q^{73} \) \(\mathstrut -\mathstrut 22261000608q^{75} \) \(\mathstrut +\mathstrut 75518805600q^{77} \) \(\mathstrut -\mathstrut 35976619976q^{79} \) \(\mathstrut +\mathstrut 6973568802q^{81} \) \(\mathstrut -\mathstrut 3501565200q^{83} \) \(\mathstrut -\mathstrut 38434553784q^{85} \) \(\mathstrut -\mathstrut 13860768600q^{87} \) \(\mathstrut -\mathstrut 55164907980q^{89} \) \(\mathstrut +\mathstrut 101443739600q^{91} \) \(\mathstrut +\mathstrut 22426810200q^{93} \) \(\mathstrut +\mathstrut 3349296000q^{95} \) \(\mathstrut +\mathstrut 93399168100q^{97} \) \(\mathstrut -\mathstrut 8137424592q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(12))\) 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
12.12.a.a \(1\) \(9.220\) \(\Q\) None \(0\) \(-243\) \(9990\) \(-86128\) \(-\) \(+\) \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b \(1\) \(9.220\) \(\Q\) None \(0\) \(243\) \(2862\) \(9128\) \(-\) \(-\) \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)

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

\( S_{12}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)