## Defining parameters

 Level: $$N$$ = $$2300 = 2^{2} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$633600$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2300))$$.

Total New Old
Modular forms 161480 85702 75778
Cusp forms 155321 83978 71343
Eisenstein series 6159 1724 4435

## Trace form

 $$83978q - 131q^{2} - 8q^{3} - 123q^{4} - 322q^{5} - 195q^{6} + 8q^{7} - 107q^{8} - 242q^{9} + O(q^{10})$$ $$83978q - 131q^{2} - 8q^{3} - 123q^{4} - 322q^{5} - 195q^{6} + 8q^{7} - 107q^{8} - 242q^{9} - 144q^{10} - 123q^{12} - 246q^{13} - 123q^{14} + 4q^{15} - 227q^{16} - 237q^{17} - 147q^{18} + 13q^{19} - 164q^{20} - 399q^{21} - 112q^{22} + 10q^{23} - 286q^{24} - 238q^{25} - 379q^{26} + 43q^{27} - 123q^{28} - 193q^{29} - 156q^{30} + 13q^{31} - 91q^{32} - 217q^{33} - 101q^{34} + 16q^{35} - 156q^{36} - 260q^{37} - 128q^{38} - 52q^{39} - 264q^{40} - 448q^{41} - 213q^{42} - 76q^{43} - 186q^{44} - 462q^{45} - 185q^{46} - 60q^{47} - 295q^{48} - 322q^{49} - 364q^{50} - 28q^{51} - 209q^{52} - 266q^{53} - 295q^{54} - 80q^{55} - 260q^{56} - 363q^{57} - 176q^{58} - 34q^{59} - 356q^{60} - 330q^{61} - 223q^{62} - 27q^{63} - 183q^{64} - 222q^{65} - 324q^{66} + 66q^{67} - 160q^{68} - 275q^{69} - 332q^{70} - 23q^{71} - 78q^{72} - 268q^{73} - 154q^{74} + 156q^{75} - 386q^{76} - 53q^{77} - 293q^{78} + 90q^{79} - 124q^{80} - 482q^{81} - 45q^{82} + 113q^{83} - 117q^{84} - 406q^{85} - 185q^{86} + 38q^{87} + 29q^{88} - 374q^{89} + 156q^{90} + 20q^{91} - 132q^{92} - 456q^{93} + 120q^{94} - 28q^{95} - 204q^{96} - 277q^{97} + 85q^{98} + 331q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2300))$$

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
2300.2.a $$\chi_{2300}(1, \cdot)$$ 2300.2.a.a 1 1
2300.2.a.b 1
2300.2.a.c 1
2300.2.a.d 1
2300.2.a.e 1
2300.2.a.f 1
2300.2.a.g 1
2300.2.a.h 1
2300.2.a.i 2
2300.2.a.j 3
2300.2.a.k 3
2300.2.a.l 4
2300.2.a.m 4
2300.2.a.n 6
2300.2.a.o 6
2300.2.c $$\chi_{2300}(1749, \cdot)$$ 2300.2.c.a 2 1
2300.2.c.b 2
2300.2.c.c 2
2300.2.c.d 2
2300.2.c.e 2
2300.2.c.f 2
2300.2.c.g 2
2300.2.c.h 4
2300.2.c.i 6
2300.2.c.j 8
2300.2.e $$\chi_{2300}(551, \cdot)$$ n/a 222 1
2300.2.g $$\chi_{2300}(2299, \cdot)$$ n/a 212 1
2300.2.i $$\chi_{2300}(1057, \cdot)$$ 2300.2.i.a 8 2
2300.2.i.b 8
2300.2.i.c 8
2300.2.i.d 16
2300.2.i.e 16
2300.2.i.f 16
2300.2.j $$\chi_{2300}(507, \cdot)$$ n/a 396 2
2300.2.m $$\chi_{2300}(461, \cdot)$$ n/a 216 4
2300.2.n $$\chi_{2300}(459, \cdot)$$ n/a 1424 4
2300.2.q $$\chi_{2300}(369, \cdot)$$ n/a 224 4
2300.2.s $$\chi_{2300}(91, \cdot)$$ n/a 1424 4
2300.2.u $$\chi_{2300}(101, \cdot)$$ n/a 380 10
2300.2.x $$\chi_{2300}(47, \cdot)$$ n/a 2640 8
2300.2.y $$\chi_{2300}(137, \cdot)$$ n/a 480 8
2300.2.ba $$\chi_{2300}(99, \cdot)$$ n/a 2120 10
2300.2.bc $$\chi_{2300}(51, \cdot)$$ n/a 2220 10
2300.2.be $$\chi_{2300}(49, \cdot)$$ n/a 360 10
2300.2.bi $$\chi_{2300}(243, \cdot)$$ n/a 4240 20
2300.2.bj $$\chi_{2300}(57, \cdot)$$ n/a 720 20
2300.2.bk $$\chi_{2300}(41, \cdot)$$ n/a 2400 40
2300.2.bm $$\chi_{2300}(11, \cdot)$$ n/a 14240 40
2300.2.bo $$\chi_{2300}(9, \cdot)$$ n/a 2400 40
2300.2.br $$\chi_{2300}(19, \cdot)$$ n/a 14240 40
2300.2.bs $$\chi_{2300}(17, \cdot)$$ n/a 4800 80
2300.2.bt $$\chi_{2300}(3, \cdot)$$ n/a 28480 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2300))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2300)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1150))$$$$^{\oplus 2}$$