# Properties

 Label 1155.2 Level 1155 Weight 2 Dimension 29305 Nonzero newspaces 48 Sturm bound 184320 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$1155 = 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$184320$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1155))$$.

Total New Old
Modular forms 48000 30393 17607
Cusp forms 44161 29305 14856
Eisenstein series 3839 1088 2751

## Trace form

 $$29305q$$ $$\mathstrut -\mathstrut 13q^{2}$$ $$\mathstrut -\mathstrut 31q^{3}$$ $$\mathstrut -\mathstrut 49q^{4}$$ $$\mathstrut +\mathstrut 13q^{5}$$ $$\mathstrut -\mathstrut 33q^{6}$$ $$\mathstrut -\mathstrut 39q^{7}$$ $$\mathstrut +\mathstrut 119q^{8}$$ $$\mathstrut +\mathstrut 41q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$29305q$$ $$\mathstrut -\mathstrut 13q^{2}$$ $$\mathstrut -\mathstrut 31q^{3}$$ $$\mathstrut -\mathstrut 49q^{4}$$ $$\mathstrut +\mathstrut 13q^{5}$$ $$\mathstrut -\mathstrut 33q^{6}$$ $$\mathstrut -\mathstrut 39q^{7}$$ $$\mathstrut +\mathstrut 119q^{8}$$ $$\mathstrut +\mathstrut 41q^{9}$$ $$\mathstrut +\mathstrut 23q^{10}$$ $$\mathstrut +\mathstrut 45q^{11}$$ $$\mathstrut +\mathstrut 47q^{12}$$ $$\mathstrut +\mathstrut 14q^{13}$$ $$\mathstrut +\mathstrut 111q^{14}$$ $$\mathstrut -\mathstrut 69q^{15}$$ $$\mathstrut +\mathstrut 119q^{16}$$ $$\mathstrut +\mathstrut 122q^{17}$$ $$\mathstrut +\mathstrut 31q^{18}$$ $$\mathstrut +\mathstrut 100q^{19}$$ $$\mathstrut +\mathstrut 147q^{20}$$ $$\mathstrut -\mathstrut 51q^{21}$$ $$\mathstrut +\mathstrut 75q^{22}$$ $$\mathstrut +\mathstrut 104q^{23}$$ $$\mathstrut +\mathstrut 3q^{24}$$ $$\mathstrut +\mathstrut 33q^{25}$$ $$\mathstrut +\mathstrut 154q^{26}$$ $$\mathstrut -\mathstrut 139q^{27}$$ $$\mathstrut +\mathstrut 15q^{28}$$ $$\mathstrut +\mathstrut 30q^{29}$$ $$\mathstrut -\mathstrut 127q^{30}$$ $$\mathstrut -\mathstrut 104q^{31}$$ $$\mathstrut -\mathstrut 153q^{32}$$ $$\mathstrut -\mathstrut 107q^{33}$$ $$\mathstrut -\mathstrut 122q^{34}$$ $$\mathstrut -\mathstrut 35q^{35}$$ $$\mathstrut -\mathstrut 409q^{36}$$ $$\mathstrut -\mathstrut 10q^{37}$$ $$\mathstrut +\mathstrut 28q^{38}$$ $$\mathstrut -\mathstrut 14q^{39}$$ $$\mathstrut -\mathstrut 325q^{40}$$ $$\mathstrut +\mathstrut 154q^{41}$$ $$\mathstrut -\mathstrut 137q^{42}$$ $$\mathstrut -\mathstrut 36q^{43}$$ $$\mathstrut +\mathstrut 39q^{44}$$ $$\mathstrut -\mathstrut 65q^{45}$$ $$\mathstrut +\mathstrut 32q^{46}$$ $$\mathstrut +\mathstrut 96q^{47}$$ $$\mathstrut -\mathstrut 181q^{48}$$ $$\mathstrut +\mathstrut 33q^{49}$$ $$\mathstrut +\mathstrut 7q^{50}$$ $$\mathstrut -\mathstrut 26q^{51}$$ $$\mathstrut -\mathstrut 262q^{52}$$ $$\mathstrut +\mathstrut 30q^{53}$$ $$\mathstrut -\mathstrut 81q^{54}$$ $$\mathstrut -\mathstrut 263q^{55}$$ $$\mathstrut -\mathstrut 89q^{56}$$ $$\mathstrut -\mathstrut 228q^{57}$$ $$\mathstrut -\mathstrut 622q^{58}$$ $$\mathstrut -\mathstrut 172q^{59}$$ $$\mathstrut -\mathstrut 647q^{60}$$ $$\mathstrut -\mathstrut 618q^{61}$$ $$\mathstrut -\mathstrut 512q^{62}$$ $$\mathstrut -\mathstrut 251q^{63}$$ $$\mathstrut -\mathstrut 1217q^{64}$$ $$\mathstrut -\mathstrut 458q^{65}$$ $$\mathstrut -\mathstrut 905q^{66}$$ $$\mathstrut -\mathstrut 668q^{67}$$ $$\mathstrut -\mathstrut 1026q^{68}$$ $$\mathstrut -\mathstrut 548q^{69}$$ $$\mathstrut -\mathstrut 941q^{70}$$ $$\mathstrut -\mathstrut 440q^{71}$$ $$\mathstrut -\mathstrut 909q^{72}$$ $$\mathstrut -\mathstrut 422q^{73}$$ $$\mathstrut -\mathstrut 542q^{74}$$ $$\mathstrut -\mathstrut 343q^{75}$$ $$\mathstrut -\mathstrut 1156q^{76}$$ $$\mathstrut -\mathstrut 275q^{77}$$ $$\mathstrut -\mathstrut 662q^{78}$$ $$\mathstrut -\mathstrut 184q^{79}$$ $$\mathstrut -\mathstrut 349q^{80}$$ $$\mathstrut -\mathstrut 543q^{81}$$ $$\mathstrut -\mathstrut 394q^{82}$$ $$\mathstrut +\mathstrut 100q^{83}$$ $$\mathstrut -\mathstrut 665q^{84}$$ $$\mathstrut -\mathstrut 182q^{85}$$ $$\mathstrut -\mathstrut 260q^{86}$$ $$\mathstrut -\mathstrut 18q^{87}$$ $$\mathstrut -\mathstrut 313q^{88}$$ $$\mathstrut +\mathstrut 26q^{89}$$ $$\mathstrut -\mathstrut 303q^{90}$$ $$\mathstrut -\mathstrut 218q^{91}$$ $$\mathstrut -\mathstrut 32q^{92}$$ $$\mathstrut -\mathstrut 12q^{93}$$ $$\mathstrut -\mathstrut 72q^{94}$$ $$\mathstrut +\mathstrut 104q^{95}$$ $$\mathstrut -\mathstrut 421q^{96}$$ $$\mathstrut +\mathstrut 98q^{97}$$ $$\mathstrut +\mathstrut 331q^{98}$$ $$\mathstrut -\mathstrut 267q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1155.2.a $$\chi_{1155}(1, \cdot)$$ 1155.2.a.a 1 1
1155.2.a.b 1
1155.2.a.c 1
1155.2.a.d 1
1155.2.a.e 1
1155.2.a.f 1
1155.2.a.g 1
1155.2.a.h 1
1155.2.a.i 1
1155.2.a.j 1
1155.2.a.k 1
1155.2.a.l 1
1155.2.a.m 1
1155.2.a.n 1
1155.2.a.o 2
1155.2.a.p 2
1155.2.a.q 2
1155.2.a.r 2
1155.2.a.s 3
1155.2.a.t 3
1155.2.a.u 4
1155.2.a.v 4
1155.2.a.w 5
1155.2.c $$\chi_{1155}(694, \cdot)$$ 1155.2.c.a 2 1
1155.2.c.b 2
1155.2.c.c 6
1155.2.c.d 6
1155.2.c.e 20
1155.2.c.f 20
1155.2.d $$\chi_{1155}(881, \cdot)$$ n/a 104 1
1155.2.f $$\chi_{1155}(659, \cdot)$$ n/a 144 1
1155.2.i $$\chi_{1155}(76, \cdot)$$ 1155.2.i.a 8 1
1155.2.i.b 8
1155.2.i.c 16
1155.2.i.d 32
1155.2.k $$\chi_{1155}(769, \cdot)$$ 1155.2.k.a 48 1
1155.2.k.b 48
1155.2.l $$\chi_{1155}(1121, \cdot)$$ 1155.2.l.a 4 1
1155.2.l.b 4
1155.2.l.c 4
1155.2.l.d 4
1155.2.l.e 40
1155.2.l.f 40
1155.2.n $$\chi_{1155}(419, \cdot)$$ n/a 160 1
1155.2.q $$\chi_{1155}(331, \cdot)$$ n/a 104 2
1155.2.s $$\chi_{1155}(617, \cdot)$$ n/a 240 2
1155.2.t $$\chi_{1155}(692, \cdot)$$ n/a 368 2
1155.2.v $$\chi_{1155}(727, \cdot)$$ n/a 160 2
1155.2.y $$\chi_{1155}(43, \cdot)$$ n/a 144 2
1155.2.z $$\chi_{1155}(421, \cdot)$$ n/a 192 4
1155.2.bb $$\chi_{1155}(296, \cdot)$$ n/a 256 2
1155.2.bc $$\chi_{1155}(439, \cdot)$$ n/a 192 2
1155.2.bg $$\chi_{1155}(89, \cdot)$$ n/a 320 2
1155.2.bi $$\chi_{1155}(551, \cdot)$$ n/a 216 2
1155.2.bj $$\chi_{1155}(529, \cdot)$$ n/a 160 2
1155.2.bl $$\chi_{1155}(241, \cdot)$$ n/a 128 2
1155.2.bo $$\chi_{1155}(494, \cdot)$$ n/a 368 2
1155.2.br $$\chi_{1155}(104, \cdot)$$ n/a 736 4
1155.2.bt $$\chi_{1155}(281, \cdot)$$ n/a 384 4
1155.2.bu $$\chi_{1155}(139, \cdot)$$ n/a 384 4
1155.2.bw $$\chi_{1155}(391, \cdot)$$ n/a 256 4
1155.2.bz $$\chi_{1155}(29, \cdot)$$ n/a 576 4
1155.2.cb $$\chi_{1155}(146, \cdot)$$ n/a 512 4
1155.2.cc $$\chi_{1155}(64, \cdot)$$ n/a 288 4
1155.2.ce $$\chi_{1155}(142, \cdot)$$ n/a 384 4
1155.2.ch $$\chi_{1155}(397, \cdot)$$ n/a 320 4
1155.2.cj $$\chi_{1155}(362, \cdot)$$ n/a 736 4
1155.2.ck $$\chi_{1155}(23, \cdot)$$ n/a 640 4
1155.2.cm $$\chi_{1155}(16, \cdot)$$ n/a 512 8
1155.2.cn $$\chi_{1155}(127, \cdot)$$ n/a 576 8
1155.2.cq $$\chi_{1155}(97, \cdot)$$ n/a 768 8
1155.2.cs $$\chi_{1155}(62, \cdot)$$ n/a 1472 8
1155.2.ct $$\chi_{1155}(92, \cdot)$$ n/a 1152 8
1155.2.cv $$\chi_{1155}(74, \cdot)$$ n/a 1472 8
1155.2.cy $$\chi_{1155}(61, \cdot)$$ n/a 512 8
1155.2.da $$\chi_{1155}(4, \cdot)$$ n/a 768 8
1155.2.db $$\chi_{1155}(26, \cdot)$$ n/a 1024 8
1155.2.dd $$\chi_{1155}(59, \cdot)$$ n/a 1472 8
1155.2.dh $$\chi_{1155}(19, \cdot)$$ n/a 768 8
1155.2.di $$\chi_{1155}(116, \cdot)$$ n/a 1024 8
1155.2.dl $$\chi_{1155}(53, \cdot)$$ n/a 2944 16
1155.2.dm $$\chi_{1155}(17, \cdot)$$ n/a 2944 16
1155.2.do $$\chi_{1155}(82, \cdot)$$ n/a 1536 16
1155.2.dr $$\chi_{1155}(172, \cdot)$$ n/a 1536 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1155))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1155)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 2}$$