Properties

Label 4.20.a
Level $4$
Weight $20$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

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

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