Properties

Label 4.6.a
Level $4$
Weight $6$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(4))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
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

\( q - 12 q^{3} + 54 q^{5} - 88 q^{7} - 99 q^{9} + O(q^{10}) \) \( q - 12 q^{3} + 54 q^{5} - 88 q^{7} - 99 q^{9} + 540 q^{11} - 418 q^{13} - 648 q^{15} + 594 q^{17} + 836 q^{19} + 1056 q^{21} - 4104 q^{23} - 209 q^{25} + 4104 q^{27} - 594 q^{29} + 4256 q^{31} - 6480 q^{33} - 4752 q^{35} - 298 q^{37} + 5016 q^{39} + 17226 q^{41} - 12100 q^{43} - 5346 q^{45} - 1296 q^{47} - 9063 q^{49} - 7128 q^{51} + 19494 q^{53} + 29160 q^{55} - 10032 q^{57} - 7668 q^{59} - 34738 q^{61} + 8712 q^{63} - 22572 q^{65} + 21812 q^{67} + 49248 q^{69} - 46872 q^{71} + 67562 q^{73} + 2508 q^{75} - 47520 q^{77} - 76912 q^{79} - 25191 q^{81} + 67716 q^{83} + 32076 q^{85} + 7128 q^{87} + 29754 q^{89} + 36784 q^{91} - 51072 q^{93} + 45144 q^{95} - 122398 q^{97} - 53460 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.6.a.a \(1\) \(0.642\) \(\Q\) None \(0\) \(-12\) \(54\) \(-88\) \(-\) \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)