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Properties

Label 44.3
Level 44
Weight 3
Dimension 60
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(44))\).

Total New Old
Modular forms 145 76 69
Cusp forms 95 60 35
Eisenstein series 50 16 34

Trace form

\( 60 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 5 q^{6} + 15 q^{7} - 5 q^{8} + O(q^{10}) \) \( 60 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 5 q^{6} + 15 q^{7} - 5 q^{8} - 10 q^{10} - 5 q^{11} - 10 q^{12} - 25 q^{13} - 40 q^{14} - 110 q^{15} - 105 q^{16} - 85 q^{17} - 80 q^{18} - 30 q^{19} - 30 q^{20} - 20 q^{21} + 25 q^{22} + 65 q^{23} + 85 q^{24} + 140 q^{25} + 120 q^{26} + 165 q^{27} + 170 q^{28} + 115 q^{29} + 220 q^{30} + 110 q^{31} + 100 q^{32} - 185 q^{33} + 170 q^{34} - 155 q^{35} + 320 q^{36} - 300 q^{37} + 120 q^{38} - 185 q^{39} + 100 q^{40} - 205 q^{41} + 30 q^{42} - 40 q^{44} + 190 q^{45} - 90 q^{46} + 145 q^{47} - 280 q^{48} + 295 q^{49} - 375 q^{50} + 150 q^{51} - 490 q^{52} + 165 q^{53} - 890 q^{54} - 100 q^{55} - 720 q^{56} - 180 q^{57} - 360 q^{58} - 285 q^{59} - 480 q^{60} - 155 q^{61} - 230 q^{62} - 110 q^{63} - 65 q^{64} - 20 q^{65} + 60 q^{66} - 25 q^{67} + 190 q^{68} + 265 q^{69} + 540 q^{70} + 340 q^{71} + 895 q^{72} + 335 q^{73} + 950 q^{74} + 390 q^{75} + 870 q^{76} + 555 q^{77} + 1180 q^{78} + 235 q^{79} + 980 q^{80} + 370 q^{81} + 585 q^{82} + 210 q^{83} + 340 q^{84} + 175 q^{85} + 55 q^{86} - 85 q^{88} + 55 q^{89} - 670 q^{90} - 195 q^{91} - 550 q^{92} - 740 q^{93} - 950 q^{94} - 255 q^{95} - 1320 q^{96} - 495 q^{97} - 1220 q^{98} - 540 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
44.3.b \(\chi_{44}(23, \cdot)\) 44.3.b.a 10 1
44.3.d \(\chi_{44}(21, \cdot)\) 44.3.d.a 2 1
44.3.f \(\chi_{44}(13, \cdot)\) 44.3.f.a 8 4
44.3.h \(\chi_{44}(3, \cdot)\) 44.3.h.a 40 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(44))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(44)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 1}\)