↑

Properties

Label 444.2
Level 444
Weight 2
Dimension 2322
Nonzero newspaces 18
Newform subspaces 50
Sturm bound 21888
Trace bound 10

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 50 \)
Sturm bound: \(21888\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(444))\).

Total New Old
Modular forms 5832 2458 3374
Cusp forms 5113 2322 2791
Eisenstein series 719 136 583

Trace form

\( 2322 q - 36 q^{4} - 18 q^{6} - 36 q^{9} + O(q^{10}) \) \( 2322 q - 36 q^{4} - 18 q^{6} - 36 q^{9} - 36 q^{10} - 18 q^{12} - 72 q^{13} - 36 q^{16} - 18 q^{18} - 36 q^{21} - 36 q^{22} - 18 q^{24} - 72 q^{25} + 6 q^{27} - 36 q^{28} + 36 q^{29} - 18 q^{30} + 108 q^{31} - 36 q^{34} + 108 q^{35} - 36 q^{36} + 12 q^{37} + 42 q^{39} - 36 q^{40} + 108 q^{41} - 18 q^{42} + 72 q^{43} - 36 q^{45} - 36 q^{46} + 36 q^{47} - 18 q^{48} - 24 q^{49} - 36 q^{52} - 18 q^{54} - 36 q^{57} - 72 q^{58} - 72 q^{59} - 144 q^{60} - 162 q^{61} - 180 q^{62} - 108 q^{63} - 288 q^{64} - 162 q^{65} - 270 q^{66} - 72 q^{67} - 216 q^{68} - 180 q^{69} - 432 q^{70} - 144 q^{71} - 270 q^{72} - 288 q^{73} - 288 q^{74} - 180 q^{75} - 324 q^{76} - 144 q^{77} - 270 q^{78} - 144 q^{79} - 396 q^{80} - 180 q^{81} - 252 q^{82} - 72 q^{83} - 270 q^{84} - 234 q^{85} - 252 q^{86} - 108 q^{87} - 216 q^{88} - 90 q^{89} - 144 q^{90} - 72 q^{91} - 36 q^{92} - 90 q^{93} - 36 q^{94} - 18 q^{96} - 72 q^{97} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)

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
444.2.a \(\chi_{444}(1, \cdot)\) 444.2.a.a 1 1
444.2.a.b 1
444.2.a.c 2
444.2.a.d 2
444.2.c \(\chi_{444}(371, \cdot)\) 444.2.c.a 8 1
444.2.c.b 8
444.2.c.c 20
444.2.c.d 36
444.2.e \(\chi_{444}(73, \cdot)\) 444.2.e.a 4 1
444.2.e.b 4
444.2.g \(\chi_{444}(443, \cdot)\) 444.2.g.a 4 1
444.2.g.b 4
444.2.g.c 16
444.2.g.d 48
444.2.i \(\chi_{444}(121, \cdot)\) 444.2.i.a 2 2
444.2.i.b 4
444.2.i.c 6
444.2.k \(\chi_{444}(31, \cdot)\) 444.2.k.a 2 2
444.2.k.b 2
444.2.k.c 36
444.2.k.d 36
444.2.m \(\chi_{444}(401, \cdot)\) 444.2.m.a 4 2
444.2.m.b 4
444.2.m.c 4
444.2.m.d 12
444.2.p \(\chi_{444}(11, \cdot)\) 444.2.p.a 4 2
444.2.p.b 4
444.2.p.c 136
444.2.r \(\chi_{444}(85, \cdot)\) 444.2.r.a 2 2
444.2.r.b 2
444.2.r.c 4
444.2.r.d 8
444.2.t \(\chi_{444}(47, \cdot)\) 444.2.t.a 144 2
444.2.u \(\chi_{444}(49, \cdot)\) 444.2.u.a 12 6
444.2.u.b 18
444.2.w \(\chi_{444}(29, \cdot)\) 444.2.w.a 4 4
444.2.w.b 4
444.2.w.c 40
444.2.y \(\chi_{444}(103, \cdot)\) 444.2.y.a 8 4
444.2.y.b 8
444.2.y.c 68
444.2.y.d 68
444.2.z \(\chi_{444}(71, \cdot)\) 444.2.z.a 432 6
444.2.ba \(\chi_{444}(95, \cdot)\) 444.2.ba.a 432 6
444.2.bb \(\chi_{444}(25, \cdot)\) 444.2.bb.a 18 6
444.2.bb.b 24
444.2.bg \(\chi_{444}(5, \cdot)\) 444.2.bg.a 12 12
444.2.bg.b 144
444.2.bh \(\chi_{444}(19, \cdot)\) 444.2.bh.a 228 12
444.2.bh.b 228

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(444))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(444)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)