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Properties

Label 1441.4
Level 1441
Weight 4
Dimension 251920
Nonzero newspaces 28
Sturm bound 686400
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1441 = 11 \cdot 131 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(686400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1441))\).

Total New Old
Modular forms 258700 254244 4456
Cusp forms 256100 251920 4180
Eisenstein series 2600 2324 276

Trace form

\( 251920 q - 510 q^{2} - 510 q^{3} - 510 q^{4} - 510 q^{5} - 410 q^{6} - 490 q^{7} - 590 q^{8} - 670 q^{9} + O(q^{10}) \) \( 251920 q - 510 q^{2} - 510 q^{3} - 510 q^{4} - 510 q^{5} - 410 q^{6} - 490 q^{7} - 590 q^{8} - 670 q^{9} - 700 q^{10} - 675 q^{11} - 1470 q^{12} - 550 q^{13} - 120 q^{14} + 110 q^{15} + 250 q^{16} - 210 q^{17} - 500 q^{18} - 960 q^{19} - 1380 q^{20} - 1340 q^{21} - 1835 q^{22} - 950 q^{23} - 130 q^{24} - 390 q^{25} - 160 q^{26} - 300 q^{27} - 180 q^{28} - 410 q^{29} + 240 q^{30} + 270 q^{31} - 960 q^{32} - 165 q^{33} - 470 q^{34} - 650 q^{35} - 600 q^{36} - 790 q^{37} - 1280 q^{38} - 2050 q^{39} - 600 q^{40} - 1530 q^{41} - 580 q^{42} + 900 q^{43} + 1655 q^{44} - 2930 q^{45} - 2300 q^{46} - 1690 q^{47} - 3360 q^{48} - 2490 q^{49} - 690 q^{50} + 300 q^{51} + 1780 q^{52} + 3450 q^{53} + 5900 q^{54} + 2625 q^{55} + 1710 q^{56} + 2300 q^{57} - 2920 q^{58} - 3140 q^{59} - 3920 q^{60} - 1150 q^{61} - 5700 q^{62} - 880 q^{63} - 1910 q^{64} - 2340 q^{65} - 3185 q^{66} - 2850 q^{67} - 3220 q^{68} - 2360 q^{69} - 800 q^{70} - 1450 q^{71} - 870 q^{72} + 4590 q^{73} + 2420 q^{74} + 840 q^{75} - 900 q^{76} + 3885 q^{77} + 2390 q^{78} + 570 q^{79} + 6400 q^{80} + 2120 q^{81} + 5450 q^{82} - 1560 q^{83} + 1120 q^{84} - 6190 q^{85} - 2330 q^{86} - 7540 q^{87} - 9935 q^{88} - 5050 q^{89} - 220 q^{90} - 3350 q^{91} + 4460 q^{92} + 4910 q^{93} + 60 q^{94} - 3790 q^{95} - 1120 q^{96} - 2220 q^{97} - 4260 q^{98} - 3815 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1441))\)

We only show spaces with even 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
1441.4.a \(\chi_{1441}(1, \cdot)\) 1441.4.a.a 77 1
1441.4.a.b 79
1441.4.a.c 84
1441.4.a.d 86
1441.4.d \(\chi_{1441}(1440, \cdot)\) n/a 394 1
1441.4.e \(\chi_{1441}(89, \cdot)\) n/a 1320 4
1441.4.f \(\chi_{1441}(394, \cdot)\) n/a 1560 4
1441.4.g \(\chi_{1441}(58, \cdot)\) n/a 1576 4
1441.4.h \(\chi_{1441}(53, \cdot)\) n/a 1576 4
1441.4.i \(\chi_{1441}(708, \cdot)\) n/a 1576 4
1441.4.j \(\chi_{1441}(192, \cdot)\) n/a 1576 4
1441.4.m \(\chi_{1441}(864, \cdot)\) n/a 1576 4
1441.4.n \(\chi_{1441}(340, \cdot)\) n/a 1576 4
1441.4.o \(\chi_{1441}(261, \cdot)\) n/a 1576 4
1441.4.p \(\chi_{1441}(73, \cdot)\) n/a 1576 4
1441.4.q \(\chi_{1441}(173, \cdot)\) n/a 1576 4
1441.4.bb \(\chi_{1441}(304, \cdot)\) n/a 1576 4
1441.4.bc \(\chi_{1441}(45, \cdot)\) n/a 3960 12
1441.4.bd \(\chi_{1441}(32, \cdot)\) n/a 4728 12
1441.4.bg \(\chi_{1441}(36, \cdot)\) n/a 18912 48
1441.4.bh \(\chi_{1441}(20, \cdot)\) n/a 18912 48
1441.4.bi \(\chi_{1441}(4, \cdot)\) n/a 18912 48
1441.4.bj \(\chi_{1441}(3, \cdot)\) n/a 18912 48
1441.4.bk \(\chi_{1441}(60, \cdot)\) n/a 18912 48
1441.4.bl \(\chi_{1441}(12, \cdot)\) n/a 15840 48
1441.4.bm \(\chi_{1441}(6, \cdot)\) n/a 18912 48
1441.4.bx \(\chi_{1441}(29, \cdot)\) n/a 18912 48
1441.4.by \(\chi_{1441}(2, \cdot)\) n/a 18912 48
1441.4.bz \(\chi_{1441}(18, \cdot)\) n/a 18912 48
1441.4.ca \(\chi_{1441}(10, \cdot)\) n/a 18912 48
1441.4.cb \(\chi_{1441}(83, \cdot)\) n/a 18912 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1441))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1441)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 2}\)