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Properties

Label 1444.2
Level 1444
Weight 2
Dimension 37227
Nonzero newspaces 12
Sturm bound 259920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(259920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1444))\).

Total New Old
Modular forms 66240 38163 28077
Cusp forms 63721 37227 26494
Eisenstein series 2519 936 1583

Trace form

\( 37227 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} + O(q^{10}) \) \( 37227 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} - 153 q^{10} - 153 q^{12} - 282 q^{13} - 153 q^{14} + 36 q^{15} - 153 q^{16} - 288 q^{17} - 171 q^{18} + 21 q^{19} - 297 q^{20} - 264 q^{21} - 153 q^{22} + 18 q^{23} - 153 q^{24} - 270 q^{25} - 153 q^{26} + 6 q^{27} - 207 q^{28} - 342 q^{29} - 279 q^{30} - 36 q^{31} - 243 q^{32} - 414 q^{33} - 243 q^{34} - 72 q^{35} - 333 q^{36} - 378 q^{37} - 225 q^{38} - 108 q^{39} - 279 q^{40} - 342 q^{41} - 333 q^{42} - 66 q^{43} - 243 q^{44} - 360 q^{45} - 243 q^{46} + 18 q^{47} - 279 q^{48} - 300 q^{49} - 207 q^{50} + 72 q^{51} - 153 q^{52} - 234 q^{53} - 99 q^{54} + 72 q^{55} - 171 q^{56} - 279 q^{57} - 297 q^{58} + 90 q^{59} - 171 q^{60} - 318 q^{61} - 63 q^{62} + 24 q^{63} - 9 q^{64} - 324 q^{65} - 9 q^{66} - 30 q^{67} - 27 q^{68} - 540 q^{69} + 63 q^{70} + 18 q^{71} + 117 q^{72} - 462 q^{73} - 45 q^{74} - 84 q^{75} - 72 q^{76} - 828 q^{77} - 9 q^{78} - 48 q^{79} - 9 q^{80} - 396 q^{81} + 117 q^{82} + 18 q^{83} + 63 q^{84} - 522 q^{85} - 27 q^{86} + 72 q^{87} - 9 q^{88} - 360 q^{89} - 99 q^{90} + 24 q^{91} - 63 q^{92} - 246 q^{93} - 171 q^{94} - 9 q^{95} - 441 q^{96} - 324 q^{97} - 351 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)

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
1444.2.a \(\chi_{1444}(1, \cdot)\) 1444.2.a.a 1 1
1444.2.a.b 1
1444.2.a.c 1
1444.2.a.d 2
1444.2.a.e 2
1444.2.a.f 2
1444.2.a.g 6
1444.2.a.h 6
1444.2.a.i 8
1444.2.d \(\chi_{1444}(1443, \cdot)\) n/a 154 1
1444.2.e \(\chi_{1444}(429, \cdot)\) 1444.2.e.a 2 2
1444.2.e.b 2
1444.2.e.c 2
1444.2.e.d 4
1444.2.e.e 4
1444.2.e.f 4
1444.2.e.g 12
1444.2.e.h 12
1444.2.e.i 16
1444.2.f \(\chi_{1444}(791, \cdot)\) n/a 308 2
1444.2.i \(\chi_{1444}(245, \cdot)\) n/a 168 6
1444.2.k \(\chi_{1444}(127, \cdot)\) n/a 924 6
1444.2.m \(\chi_{1444}(77, \cdot)\) n/a 558 18
1444.2.n \(\chi_{1444}(75, \cdot)\) n/a 3384 18
1444.2.q \(\chi_{1444}(45, \cdot)\) n/a 1116 36
1444.2.t \(\chi_{1444}(27, \cdot)\) n/a 6768 36
1444.2.u \(\chi_{1444}(5, \cdot)\) n/a 3456 108
1444.2.w \(\chi_{1444}(3, \cdot)\) n/a 20304 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

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