Properties

Label 900.4.i
Level 900900
Weight 44
Character orbit 900.i
Rep. character χ900(301,)\chi_{900}(301,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 114114
Sturm bound 720720

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Defining parameters

Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 900.i (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 9 9
Character field: Q(ζ3)\Q(\zeta_{3})
Sturm bound: 720720

Dimensions

The following table gives the dimensions of various subspaces of M4(900,[χ])M_{4}(900, [\chi]).

Total New Old
Modular forms 1116 114 1002
Cusp forms 1044 114 930
Eisenstein series 72 0 72

Trace form

114q+q36q729q9q11+12q13126q17+30q1980q21126q2356q27336q29+12q31135q33240q37+516q39427q41+129q43+856q99+O(q100) 114 q + q^{3} - 6 q^{7} - 29 q^{9} - q^{11} + 12 q^{13} - 126 q^{17} + 30 q^{19} - 80 q^{21} - 126 q^{23} - 56 q^{27} - 336 q^{29} + 12 q^{31} - 135 q^{33} - 240 q^{37} + 516 q^{39} - 427 q^{41} + 129 q^{43}+ \cdots - 856 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(900,[χ])S_{4}^{\mathrm{new}}(900, [\chi]) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of S4old(900,[χ])S_{4}^{\mathrm{old}}(900, [\chi]) into lower level spaces