Properties

Label 45.22
Level 45
Weight 22
Dimension 1083
Nonzero newspaces 6
Sturm bound 3168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(3168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(45))\).

Total New Old
Modular forms 1544 1109 435
Cusp forms 1480 1083 397
Eisenstein series 64 26 38

Trace form

\( 1083 q - 2504 q^{2} - 257690 q^{3} + 21200338 q^{4} - 41769246 q^{5} - 374230078 q^{6} + 241175512 q^{7} - 7838850384 q^{8} - 26890838278 q^{9} + O(q^{10}) \) \( 1083 q - 2504 q^{2} - 257690 q^{3} + 21200338 q^{4} - 41769246 q^{5} - 374230078 q^{6} + 241175512 q^{7} - 7838850384 q^{8} - 26890838278 q^{9} + 44875769126 q^{10} - 565642789220 q^{11} + 1600712548016 q^{12} - 2149948575960 q^{13} + 7052347043436 q^{14} - 1293880241219 q^{15} + 69589149210122 q^{16} + 28612908102502 q^{17} - 112517108771984 q^{18} + 49663453047488 q^{19} - 235332921973180 q^{20} - 40726520165010 q^{21} - 166148602999274 q^{22} - 917340025776336 q^{23} - 291286961158422 q^{24} - 5622731338477344 q^{25} - 6514385786634524 q^{26} + 4123575019502080 q^{27} - 3550183730723464 q^{28} + 5480182568948588 q^{29} - 12102149921688232 q^{30} + 1080995071706330 q^{31} - 46795494918463378 q^{32} + 29010488961466904 q^{33} - 58974612419878738 q^{34} - 62854483639928944 q^{35} + 172133632385286058 q^{36} + 38510163182170322 q^{37} - 32744331475346570 q^{38} + 602976614783053978 q^{39} - 168379105989344460 q^{40} + 401139158719551290 q^{41} + 512828628081774816 q^{42} + 57778617248794326 q^{43} - 1524220960407253132 q^{44} + 622659442345859459 q^{45} - 2417219604768400552 q^{46} - 2330183481369346256 q^{47} + 1491005285560061594 q^{48} - 43446524354598767 q^{49} + 2751638226534317470 q^{50} + 909281020093766582 q^{51} + 1234713030698624432 q^{52} + 788814076280197954 q^{53} + 19843909366119215906 q^{54} + 4489336522809084786 q^{55} - 40652145023271326676 q^{56} + 27160529946873066622 q^{57} + 26573591728107079000 q^{58} + 11548483136242715356 q^{59} - 40606299300836445808 q^{60} - 21825831266759840396 q^{61} + 86982037438225595676 q^{62} + 30023081358543495642 q^{63} - 101555169168351117172 q^{64} - 8794559836012134449 q^{65} + 134692366487228903428 q^{66} + 15889141764093734914 q^{67} - 57642387810418224754 q^{68} - 164148316630604812350 q^{69} - 152543903474329141446 q^{70} + 224712412460535292964 q^{71} + 59045050129246663338 q^{72} - 117569868368351269002 q^{73} - 260033646621884745388 q^{74} + 232082977249206125569 q^{75} - 253017388243900534970 q^{76} + 195433900811517054090 q^{77} - 847608010053959357548 q^{78} - 34090497850996499346 q^{79} + 1532933728070805813272 q^{80} + 1088489221360259262650 q^{81} - 1861423997902482276096 q^{82} - 1237830908509660843440 q^{83} - 595818347049491840580 q^{84} + 225472090051889494496 q^{85} + 2330727461937279561022 q^{86} - 305809132558050892778 q^{87} - 1768267165393791199722 q^{88} - 2176291877446422014310 q^{89} - 2752105804204145362652 q^{90} + 881481992534379158336 q^{91} + 7415769179862220864764 q^{92} + 1452281639214325126230 q^{93} - 4291017814239246616204 q^{94} - 8967637737732390922124 q^{95} + 4513020287001072154048 q^{96} + 2946105436058005467890 q^{97} + 2264878733223957887918 q^{98} - 1638778208836740681302 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.22.a \(\chi_{45}(1, \cdot)\) 45.22.a.a 1 1
45.22.a.b 3
45.22.a.c 3
45.22.a.d 3
45.22.a.e 3
45.22.a.f 4
45.22.a.g 4
45.22.a.h 7
45.22.a.i 7
45.22.b \(\chi_{45}(19, \cdot)\) 45.22.b.a 2 1
45.22.b.b 10
45.22.b.c 20
45.22.b.d 20
45.22.e \(\chi_{45}(16, \cdot)\) n/a 168 2
45.22.f \(\chi_{45}(8, \cdot)\) 45.22.f.a 84 2
45.22.j \(\chi_{45}(4, \cdot)\) n/a 248 2
45.22.l \(\chi_{45}(2, \cdot)\) n/a 496 4

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

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)