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Properties

Label 1936.2
Level 1936
Weight 2
Dimension 63632
Nonzero newspaces 16
Sturm bound 464640
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1936 = 2^{4} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(464640\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1936))\).

Total New Old
Modular forms 118400 64897 53503
Cusp forms 113921 63632 50289
Eisenstein series 4479 1265 3214

Trace form

\( 63632 q - 182 q^{2} - 137 q^{3} - 180 q^{4} - 227 q^{5} - 176 q^{6} - 135 q^{7} - 176 q^{8} - 45 q^{9} + O(q^{10}) \) \( 63632 q - 182 q^{2} - 137 q^{3} - 180 q^{4} - 227 q^{5} - 176 q^{6} - 135 q^{7} - 176 q^{8} - 45 q^{9} - 180 q^{10} - 150 q^{11} - 344 q^{12} - 227 q^{13} - 184 q^{14} - 131 q^{15} - 188 q^{16} - 409 q^{17} - 178 q^{18} - 129 q^{19} - 176 q^{20} - 211 q^{21} - 200 q^{22} - 255 q^{23} - 180 q^{24} - 45 q^{25} - 176 q^{26} - 143 q^{27} - 172 q^{28} - 219 q^{29} - 184 q^{30} - 151 q^{31} - 172 q^{32} - 430 q^{33} - 336 q^{34} - 79 q^{35} - 184 q^{36} - 179 q^{37} - 192 q^{38} - 15 q^{39} - 188 q^{40} + 35 q^{41} - 180 q^{42} - 75 q^{43} - 200 q^{44} - 303 q^{45} - 168 q^{46} - 59 q^{47} - 172 q^{48} - 319 q^{49} - 186 q^{50} - 11 q^{51} - 184 q^{52} - 195 q^{53} - 180 q^{54} - 120 q^{55} - 348 q^{56} - 5 q^{57} - 192 q^{58} - 141 q^{59} - 180 q^{60} - 243 q^{61} - 164 q^{62} - 161 q^{63} - 180 q^{64} - 391 q^{65} - 200 q^{66} - 265 q^{67} - 180 q^{68} - 207 q^{69} - 452 q^{70} - 155 q^{71} - 376 q^{72} - 205 q^{73} - 380 q^{74} - 209 q^{75} - 488 q^{76} - 330 q^{77} - 824 q^{78} - 235 q^{79} - 612 q^{80} - 635 q^{81} - 580 q^{82} - 237 q^{83} - 668 q^{84} - 541 q^{85} - 500 q^{86} - 305 q^{87} - 520 q^{88} - 245 q^{89} - 824 q^{90} - 251 q^{91} - 524 q^{92} - 529 q^{93} - 676 q^{94} - 247 q^{95} - 596 q^{96} - 649 q^{97} - 626 q^{98} - 200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)

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
1936.2.a \(\chi_{1936}(1, \cdot)\) 1936.2.a.a 1 1
1936.2.a.b 1
1936.2.a.c 1
1936.2.a.d 1
1936.2.a.e 1
1936.2.a.f 1
1936.2.a.g 1
1936.2.a.h 1
1936.2.a.i 1
1936.2.a.j 1
1936.2.a.k 1
1936.2.a.l 1
1936.2.a.m 2
1936.2.a.n 2
1936.2.a.o 2
1936.2.a.p 2
1936.2.a.q 2
1936.2.a.r 2
1936.2.a.s 2
1936.2.a.t 2
1936.2.a.u 2
1936.2.a.v 2
1936.2.a.w 2
1936.2.a.x 2
1936.2.a.y 2
1936.2.a.z 2
1936.2.a.ba 2
1936.2.a.bb 4
1936.2.a.bc 4
1936.2.c \(\chi_{1936}(969, \cdot)\) None 0 1
1936.2.e \(\chi_{1936}(1935, \cdot)\) 1936.2.e.a 2 1
1936.2.e.b 4
1936.2.e.c 4
1936.2.e.d 4
1936.2.e.e 8
1936.2.e.f 16
1936.2.e.g 16
1936.2.g \(\chi_{1936}(967, \cdot)\) None 0 1
1936.2.i \(\chi_{1936}(483, \cdot)\) n/a 416 2
1936.2.j \(\chi_{1936}(485, \cdot)\) n/a 418 2
1936.2.m \(\chi_{1936}(81, \cdot)\) n/a 200 4
1936.2.o \(\chi_{1936}(215, \cdot)\) None 0 4
1936.2.q \(\chi_{1936}(239, \cdot)\) n/a 216 4
1936.2.s \(\chi_{1936}(9, \cdot)\) None 0 4
1936.2.u \(\chi_{1936}(177, \cdot)\) n/a 650 10
1936.2.x \(\chi_{1936}(245, \cdot)\) n/a 1664 8
1936.2.y \(\chi_{1936}(403, \cdot)\) n/a 1664 8
1936.2.z \(\chi_{1936}(175, \cdot)\) n/a 660 10
1936.2.bb \(\chi_{1936}(89, \cdot)\) None 0 10
1936.2.be \(\chi_{1936}(87, \cdot)\) None 0 10
1936.2.bi \(\chi_{1936}(45, \cdot)\) n/a 5240 20
1936.2.bj \(\chi_{1936}(43, \cdot)\) n/a 5240 20
1936.2.bk \(\chi_{1936}(49, \cdot)\) n/a 2600 40
1936.2.bm \(\chi_{1936}(7, \cdot)\) None 0 40
1936.2.bp \(\chi_{1936}(25, \cdot)\) None 0 40
1936.2.br \(\chi_{1936}(63, \cdot)\) n/a 2640 40
1936.2.bs \(\chi_{1936}(19, \cdot)\) n/a 20960 80
1936.2.bt \(\chi_{1936}(5, \cdot)\) n/a 20960 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1936)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)