Properties

Label 4.20.a
Level 4
Weight 20
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(4))\).

Total New Old
Modular forms 11 1 10
Cusp forms 8 1 7
Eisenstein series 3 0 3

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.
\(-\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 36q^{3} \) \(\mathstrut -\mathstrut 196290q^{5} \) \(\mathstrut -\mathstrut 35905576q^{7} \) \(\mathstrut -\mathstrut 1162260171q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 36q^{3} \) \(\mathstrut -\mathstrut 196290q^{5} \) \(\mathstrut -\mathstrut 35905576q^{7} \) \(\mathstrut -\mathstrut 1162260171q^{9} \) \(\mathstrut -\mathstrut 12016099980q^{11} \) \(\mathstrut -\mathstrut 45529656874q^{13} \) \(\mathstrut +\mathstrut 7066440q^{15} \) \(\mathstrut +\mathstrut 496563248178q^{17} \) \(\mathstrut +\mathstrut 1410273986444q^{19} \) \(\mathstrut +\mathstrut 1292600736q^{21} \) \(\mathstrut -\mathstrut 7039745388792q^{23} \) \(\mathstrut -\mathstrut 19034956564025q^{25} \) \(\mathstrut +\mathstrut 83682778968q^{27} \) \(\mathstrut +\mathstrut 38996890912134q^{29} \) \(\mathstrut +\mathstrut 173641323230816q^{31} \) \(\mathstrut +\mathstrut 432579599280q^{33} \) \(\mathstrut +\mathstrut 7047905513040q^{35} \) \(\mathstrut -\mathstrut 1108106825662306q^{37} \) \(\mathstrut +\mathstrut 1639067647464q^{39} \) \(\mathstrut -\mathstrut 1444509198124614q^{41} \) \(\mathstrut +\mathstrut 4646075748354260q^{43} \) \(\mathstrut +\mathstrut 228140048965590q^{45} \) \(\mathstrut +\mathstrut 8950457686524048q^{47} \) \(\mathstrut -\mathstrut 10109684797481367q^{49} \) \(\mathstrut -\mathstrut 17876276934408q^{51} \) \(\mathstrut -\mathstrut 32948524384463538q^{53} \) \(\mathstrut +\mathstrut 2358640265074200q^{55} \) \(\mathstrut -\mathstrut 50769863511984q^{57} \) \(\mathstrut +\mathstrut 36999205673523588q^{59} \) \(\mathstrut +\mathstrut 82929105285760742q^{61} \) \(\mathstrut +\mathstrut 41731620901613496q^{63} \) \(\mathstrut +\mathstrut 8937016347797460q^{65} \) \(\mathstrut -\mathstrut 186668590860047716q^{67} \) \(\mathstrut +\mathstrut 253430833996512q^{69} \) \(\mathstrut -\mathstrut 596514630027659112q^{71} \) \(\mathstrut +\mathstrut 310786775495585306q^{73} \) \(\mathstrut +\mathstrut 685258436304900q^{75} \) \(\mathstrut +\mathstrut 431444991055488480q^{77} \) \(\mathstrut +\mathstrut 700397513485701872q^{79} \) \(\mathstrut +\mathstrut 1350847198802088009q^{81} \) \(\mathstrut -\mathstrut 1357882121724855732q^{83} \) \(\mathstrut -\mathstrut 97470399984859620q^{85} \) \(\mathstrut -\mathstrut 1403888072836824q^{87} \) \(\mathstrut -\mathstrut 5991411253779123894q^{89} \) \(\mathstrut +\mathstrut 1634768555143329424q^{91} \) \(\mathstrut -\mathstrut 6251087636309376q^{93} \) \(\mathstrut -\mathstrut 276822680799092760q^{95} \) \(\mathstrut +\mathstrut 4531118407744664354q^{97} \) \(\mathstrut +\mathstrut 13965834417507896580q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.20.a.a \(1\) \(9.153\) \(\Q\) None \(0\) \(-36\) \(-196290\) \(-35905576\) \(-\) \(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)