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

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

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 the 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

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