↑

Properties

Label 45.5
Level 45
Weight 5
Dimension 194
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 720
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(45))\).

Total New Old
Modular forms 320 222 98
Cusp forms 256 194 62
Eisenstein series 64 28 36

Trace form

\( 194 q - 2 q^{3} - 26 q^{4} + 48 q^{5} + 182 q^{6} + 32 q^{7} - 192 q^{8} - 346 q^{9} + O(q^{10}) \) \( 194 q - 2 q^{3} - 26 q^{4} + 48 q^{5} + 182 q^{6} + 32 q^{7} - 192 q^{8} - 346 q^{9} + 14 q^{10} - 366 q^{11} - 28 q^{12} + 1134 q^{13} + 2280 q^{14} + 670 q^{15} - 1022 q^{16} - 1806 q^{17} - 4160 q^{18} - 2780 q^{19} - 4014 q^{20} - 1992 q^{21} + 2478 q^{22} + 4668 q^{23} + 7134 q^{24} + 6110 q^{25} + 7692 q^{26} + 2284 q^{27} - 192 q^{28} + 2100 q^{29} - 1090 q^{30} - 3700 q^{31} - 8442 q^{32} - 526 q^{33} - 18862 q^{34} - 8868 q^{35} - 3470 q^{36} + 4402 q^{37} - 1434 q^{38} - 11036 q^{39} + 16258 q^{40} - 10242 q^{41} - 24612 q^{42} - 2070 q^{43} + 5264 q^{45} + 1224 q^{46} + 10128 q^{47} + 31694 q^{48} + 3390 q^{49} + 21912 q^{50} + 16670 q^{51} + 18808 q^{52} + 31434 q^{53} + 26222 q^{54} + 23608 q^{55} + 25332 q^{56} - 17342 q^{57} - 10792 q^{58} - 31722 q^{59} - 42010 q^{60} - 49212 q^{61} - 53940 q^{62} - 4872 q^{63} - 46532 q^{64} - 19620 q^{65} + 21028 q^{66} + 10190 q^{67} + 27990 q^{68} + 28368 q^{69} + 25200 q^{70} + 21312 q^{71} + 44538 q^{72} + 25374 q^{73} + 44100 q^{74} + 22876 q^{75} + 8142 q^{76} - 17220 q^{77} - 33208 q^{78} + 9492 q^{79} - 129600 q^{80} - 118606 q^{81} - 20540 q^{82} - 59004 q^{83} - 132516 q^{84} + 10160 q^{85} - 41682 q^{86} - 9164 q^{87} - 54522 q^{88} + 28426 q^{90} - 44480 q^{91} + 101880 q^{92} + 60408 q^{93} - 5644 q^{94} + 102702 q^{95} + 219184 q^{96} + 58588 q^{97} + 149382 q^{98} + 98080 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with odd 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
45.5.c \(\chi_{45}(26, \cdot)\) 45.5.c.a 4 1
45.5.d \(\chi_{45}(44, \cdot)\) 45.5.d.a 8 1
45.5.g \(\chi_{45}(28, \cdot)\) 45.5.g.a 2 2
45.5.g.b 2
45.5.g.c 2
45.5.g.d 4
45.5.g.e 8
45.5.h \(\chi_{45}(14, \cdot)\) 45.5.h.a 44 2
45.5.i \(\chi_{45}(11, \cdot)\) 45.5.i.a 32 2
45.5.k \(\chi_{45}(7, \cdot)\) 45.5.k.a 88 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)