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Properties

Label 4.18.a
Level $4$
Weight $18$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(4))\).

Total New Old
Modular forms 10 2 8
Cusp forms 7 2 5
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
\(-\)\(2\)

Trace form

\( 2 q - 5880 q^{3} + 604044 q^{5} + 25350160 q^{7} + 449174682 q^{9} + O(q^{10}) \) \( 2 q - 5880 q^{3} + 604044 q^{5} + 25350160 q^{7} + 449174682 q^{9} + 1259648280 q^{11} - 1320052580 q^{13} - 26621930448 q^{15} - 27498226140 q^{17} + 101133633832 q^{19} + 335430207552 q^{21} + 134767491120 q^{23} - 448986850114 q^{25} - 4619416117680 q^{27} + 2337155582652 q^{29} + 278836113472 q^{31} + 22602380058720 q^{33} - 7102242382752 q^{35} + 20929802888140 q^{37} - 108447997173648 q^{39} + 4166592315732 q^{41} - 111143148534440 q^{43} + 281755357404444 q^{45} + 196772651157600 q^{47} + 99570326741874 q^{49} - 39956666918256 q^{51} - 487965122736660 q^{53} - 566565363246960 q^{55} - 2272313631999840 q^{57} + 2835904197813624 q^{59} - 67544034994436 q^{61} + 3282762121966800 q^{63} + 3645157343001768 q^{65} - 995171321546360 q^{67} - 10188302100105024 q^{69} + 3882245493215376 q^{71} - 12746425881769580 q^{73} - 13688080703624712 q^{75} + 31591755846002880 q^{77} - 14984271534065504 q^{79} + 33380230287529458 q^{81} + 43899417809893800 q^{83} - 3956216991540264 q^{85} - 100892756486768400 q^{87} + 51909007958846388 q^{89} - 83455169400462112 q^{91} - 89807116632334080 q^{93} + 101643889304423664 q^{95} - 49281007789848380 q^{97} + 128223271309133880 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
4.18.a.a 4.a 1.a $2$ $7.329$ \(\Q(\sqrt{9361}) \) None \(0\) \(-5880\) \(604044\) \(25350160\) $-$ $\mathrm{SU}(2)$ \(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)