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Properties

Label 144.6
Level 144
Weight 6
Dimension 1262
Nonzero newspaces 8
Sturm bound 6912
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(6912\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(144))\).

Total New Old
Modular forms 2992 1303 1689
Cusp forms 2768 1262 1506
Eisenstein series 224 41 183

Trace form

\( 1262 q - 6 q^{2} - 6 q^{3} - 28 q^{4} - 25 q^{5} - 8 q^{6} - 15 q^{7} + 240 q^{8} - 46 q^{9} + O(q^{10}) \) \( 1262 q - 6 q^{2} - 6 q^{3} - 28 q^{4} - 25 q^{5} - 8 q^{6} - 15 q^{7} + 240 q^{8} - 46 q^{9} - 452 q^{10} + 177 q^{11} - 8 q^{12} + 285 q^{13} - 360 q^{14} - 1683 q^{15} - 5756 q^{16} + 1390 q^{17} + 8012 q^{18} - 658 q^{19} + 6272 q^{20} - 3047 q^{21} - 15696 q^{22} - 2441 q^{23} - 16168 q^{24} - 5646 q^{25} + 3844 q^{26} + 6168 q^{27} + 25816 q^{28} + 39991 q^{29} + 31172 q^{30} - 5617 q^{31} - 16356 q^{32} - 20631 q^{33} - 57024 q^{34} - 40590 q^{35} + 30324 q^{36} + 4734 q^{37} - 15580 q^{38} + 58161 q^{39} - 44988 q^{40} + 31557 q^{41} - 30448 q^{42} - 20487 q^{43} + 32824 q^{44} + 8703 q^{45} + 33852 q^{46} - 183243 q^{47} + 112364 q^{48} - 59690 q^{49} + 42714 q^{50} - 57110 q^{51} + 55024 q^{52} + 55900 q^{53} - 115332 q^{54} + 264258 q^{55} - 54528 q^{56} + 186596 q^{57} - 128668 q^{58} + 155003 q^{59} - 234380 q^{60} - 30115 q^{61} - 175848 q^{62} - 143043 q^{63} - 74200 q^{64} - 113703 q^{65} + 3712 q^{66} - 122145 q^{67} + 291088 q^{68} + 201569 q^{69} + 186988 q^{70} - 85552 q^{71} + 556520 q^{72} - 243840 q^{73} + 346448 q^{74} + 69166 q^{75} - 121120 q^{76} - 146491 q^{77} - 46412 q^{78} + 360393 q^{79} - 749600 q^{80} - 395030 q^{81} + 8520 q^{82} - 235413 q^{83} - 1105976 q^{84} + 644642 q^{85} - 252560 q^{86} - 70737 q^{87} + 127540 q^{88} + 200982 q^{89} + 614584 q^{90} - 164026 q^{91} + 691180 q^{92} - 236691 q^{93} + 360620 q^{94} + 589988 q^{95} + 607164 q^{96} - 236805 q^{97} + 378454 q^{98} + 371241 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.6.a \(\chi_{144}(1, \cdot)\) 144.6.a.a 1 1
144.6.a.b 1
144.6.a.c 1
144.6.a.d 1
144.6.a.e 1
144.6.a.f 1
144.6.a.g 1
144.6.a.h 1
144.6.a.i 1
144.6.a.j 1
144.6.a.k 1
144.6.a.l 1
144.6.c \(\chi_{144}(143, \cdot)\) 144.6.c.a 2 1
144.6.c.b 8
144.6.d \(\chi_{144}(73, \cdot)\) None 0 1
144.6.f \(\chi_{144}(71, \cdot)\) None 0 1
144.6.i \(\chi_{144}(49, \cdot)\) 144.6.i.a 4 2
144.6.i.b 6
144.6.i.c 8
144.6.i.d 10
144.6.i.e 14
144.6.i.f 16
144.6.k \(\chi_{144}(37, \cdot)\) 144.6.k.a 18 2
144.6.k.b 40
144.6.k.c 40
144.6.l \(\chi_{144}(35, \cdot)\) 144.6.l.a 80 2
144.6.p \(\chi_{144}(23, \cdot)\) None 0 2
144.6.r \(\chi_{144}(25, \cdot)\) None 0 2
144.6.s \(\chi_{144}(47, \cdot)\) 144.6.s.a 20 2
144.6.s.b 20
144.6.s.c 20
144.6.u \(\chi_{144}(11, \cdot)\) n/a 472 4
144.6.x \(\chi_{144}(13, \cdot)\) n/a 472 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)