Properties

Label 2012.2.a
Level 2012
Weight 2
Character orbit a
Rep. character \(\chi_{2012}(1,\cdot)\)
Character field \(\Q\)
Dimension 42
Newforms 2
Sturm bound 504
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2012 = 2^{2} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2012.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(504\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2012))\).

Total New Old
Modular forms 255 42 213
Cusp forms 250 42 208
Eisenstein series 5 0 5

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

\(2\)\(503\)FrickeDim.
\(-\)\(+\)\(-\)\(21\)
\(-\)\(-\)\(+\)\(21\)
Plus space\(+\)\(21\)
Minus space\(-\)\(21\)

Trace form

\(42q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(42q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 6q^{27} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 22q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut +\mathstrut 58q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 503
2012.2.a.a \(21\) \(16.066\) None \(0\) \(-10\) \(-3\) \(-15\) \(-\) \(-\)
2012.2.a.b \(21\) \(16.066\) None \(0\) \(10\) \(3\) \(13\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 2}\)