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Properties

Label 1444.3
Level 1444
Weight 3
Dimension 74922
Nonzero newspaces 12
Sturm bound 389880
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(389880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1444))\).

Total New Old
Modular forms 131220 75860 55360
Cusp forms 128700 74922 53778
Eisenstein series 2520 938 1582

Trace form

\( 74922 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} + O(q^{10}) \) \( 74922 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} - 153 q^{10} - 153 q^{12} - 426 q^{13} - 153 q^{14} - 108 q^{15} - 153 q^{16} - 324 q^{17} - 135 q^{18} + 21 q^{19} - 297 q^{20} - 180 q^{21} - 153 q^{22} + 90 q^{23} - 153 q^{24} - 54 q^{25} - 153 q^{26} + 396 q^{27} + 333 q^{28} - 18 q^{29} + 729 q^{30} + 216 q^{31} + 297 q^{32} + 126 q^{33} + 117 q^{34} + 144 q^{35} + 27 q^{36} - 270 q^{37} - 225 q^{38} - 216 q^{39} - 531 q^{40} - 450 q^{41} - 1053 q^{42} - 510 q^{43} - 783 q^{44} - 1764 q^{45} - 963 q^{46} - 846 q^{47} - 1539 q^{48} - 1032 q^{49} - 855 q^{50} - 702 q^{51} - 153 q^{52} - 522 q^{53} - 315 q^{54} - 72 q^{55} - 135 q^{56} - 279 q^{57} - 297 q^{58} + 270 q^{59} - 855 q^{60} + 1230 q^{61} - 1323 q^{62} + 1080 q^{63} - 1737 q^{64} + 1584 q^{65} - 1449 q^{66} + 1038 q^{67} - 1035 q^{68} + 2124 q^{69} - 1233 q^{70} + 954 q^{71} - 963 q^{72} + 120 q^{73} - 225 q^{74} - 72 q^{76} - 1404 q^{77} + 315 q^{78} - 876 q^{79} + 567 q^{80} - 2214 q^{81} + 1737 q^{82} - 882 q^{83} + 1791 q^{84} - 3834 q^{85} + 1233 q^{86} - 1872 q^{87} + 1719 q^{88} - 2088 q^{89} + 2457 q^{90} - 984 q^{91} + 1377 q^{92} - 1962 q^{93} + 1233 q^{94} + 675 q^{95} + 2151 q^{96} + 1008 q^{97} + 2817 q^{98} + 2484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1444))\)

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
1444.3.b \(\chi_{1444}(723, \cdot)\) n/a 324 1
1444.3.c \(\chi_{1444}(721, \cdot)\) 1444.3.c.a 6 1
1444.3.c.b 8
1444.3.c.c 18
1444.3.c.d 24
1444.3.g \(\chi_{1444}(1151, \cdot)\) n/a 648 2
1444.3.h \(\chi_{1444}(69, \cdot)\) n/a 112 2
1444.3.j \(\chi_{1444}(333, \cdot)\) n/a 342 6
1444.3.l \(\chi_{1444}(99, \cdot)\) n/a 1944 6
1444.3.o \(\chi_{1444}(37, \cdot)\) n/a 1152 18
1444.3.p \(\chi_{1444}(39, \cdot)\) n/a 6804 18
1444.3.r \(\chi_{1444}(65, \cdot)\) n/a 2304 36
1444.3.s \(\chi_{1444}(7, \cdot)\) n/a 13608 36
1444.3.v \(\chi_{1444}(23, \cdot)\) n/a 40824 108
1444.3.x \(\chi_{1444}(13, \cdot)\) n/a 6804 108

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1444)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 1}\)