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Properties

Label 1444.4
Level 1444
Weight 4
Dimension 112617
Nonzero newspaces 12
Sturm bound 519840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(519840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1444))\).

Total New Old
Modular forms 196200 113553 82647
Cusp forms 193680 112617 81063
Eisenstein series 2520 936 1584

Trace form

\( 112617 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} + O(q^{10}) \) \( 112617 q - 153 q^{2} - 153 q^{4} - 306 q^{5} - 153 q^{6} - 153 q^{8} - 306 q^{9} - 153 q^{10} - 153 q^{12} - 18 q^{13} - 153 q^{14} - 216 q^{15} - 153 q^{16} - 594 q^{17} - 171 q^{18} - 378 q^{19} - 297 q^{20} - 810 q^{21} - 153 q^{22} + 36 q^{23} - 153 q^{24} + 558 q^{25} - 153 q^{26} - 18 q^{27} - 3015 q^{28} - 1566 q^{29} - 2547 q^{30} - 180 q^{31} + 477 q^{32} + 1530 q^{33} + 2097 q^{34} + 2232 q^{35} + 6147 q^{36} + 990 q^{37} + 2169 q^{38} + 3780 q^{39} + 3753 q^{40} + 594 q^{41} + 2907 q^{42} + 1260 q^{43} - 603 q^{44} + 1746 q^{45} - 3303 q^{46} - 72 q^{47} - 9351 q^{48} - 3726 q^{49} - 6579 q^{50} - 4950 q^{51} - 153 q^{52} - 3474 q^{53} + 333 q^{54} - 3888 q^{55} - 171 q^{56} - 2844 q^{57} - 297 q^{58} - 4500 q^{59} + 5301 q^{60} - 14238 q^{61} + 9477 q^{62} - 4896 q^{63} + 8055 q^{64} - 2646 q^{65} + 2007 q^{66} + 2484 q^{67} - 2547 q^{68} + 14598 q^{69} - 9873 q^{70} + 10296 q^{71} - 17163 q^{72} + 12168 q^{73} - 10809 q^{74} + 6300 q^{75} - 6912 q^{76} + 21618 q^{77} - 12717 q^{78} + 10548 q^{79} - 8073 q^{80} + 13320 q^{81} - 9063 q^{82} + 2736 q^{83} - 801 q^{84} - 4914 q^{85} + 4257 q^{86} - 9576 q^{87} + 11511 q^{88} - 15318 q^{89} + 17037 q^{90} - 13824 q^{91} + 17577 q^{92} - 32958 q^{93} - 171 q^{94} - 10782 q^{95} - 28089 q^{96} - 16506 q^{97} - 25299 q^{98} - 22878 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1444))\)

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
1444.4.a \(\chi_{1444}(1, \cdot)\) 1444.4.a.a 1 1
1444.4.a.b 1
1444.4.a.c 2
1444.4.a.d 2
1444.4.a.e 3
1444.4.a.f 5
1444.4.a.g 5
1444.4.a.h 10
1444.4.a.i 10
1444.4.a.j 15
1444.4.a.k 15
1444.4.a.l 16
1444.4.d \(\chi_{1444}(1443, \cdot)\) n/a 494 1
1444.4.e \(\chi_{1444}(429, \cdot)\) n/a 170 2
1444.4.f \(\chi_{1444}(791, \cdot)\) n/a 988 2
1444.4.i \(\chi_{1444}(245, \cdot)\) n/a 510 6
1444.4.k \(\chi_{1444}(127, \cdot)\) n/a 2964 6
1444.4.m \(\chi_{1444}(77, \cdot)\) n/a 1710 18
1444.4.n \(\chi_{1444}(75, \cdot)\) n/a 10224 18
1444.4.q \(\chi_{1444}(45, \cdot)\) n/a 3420 36
1444.4.t \(\chi_{1444}(27, \cdot)\) n/a 20448 36
1444.4.u \(\chi_{1444}(5, \cdot)\) n/a 10260 108
1444.4.w \(\chi_{1444}(3, \cdot)\) n/a 61344 108

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

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