# Properties

 Label 3174.2 Level 3174 Weight 2 Dimension 69563 Nonzero newspaces 8 Sturm bound 1117248 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$3174 = 2 \cdot 3 \cdot 23^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$1117248$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3174))$$.

Total New Old
Modular forms 282304 69563 212741
Cusp forms 276321 69563 206758
Eisenstein series 5983 0 5983

## Trace form

 $$69563 q - q^{2} - q^{3} - q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - q^{8} - q^{9} + O(q^{10})$$ $$69563 q - q^{2} - q^{3} - q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - q^{8} - q^{9} - 6 q^{10} - 12 q^{11} - q^{12} - 14 q^{13} - 8 q^{14} + 38 q^{15} - q^{16} + 70 q^{17} + 87 q^{18} + 68 q^{19} + 82 q^{20} + 124 q^{21} + 76 q^{22} + 88 q^{23} - q^{24} + 145 q^{25} + 74 q^{26} + 131 q^{27} + 80 q^{28} + 58 q^{29} + 82 q^{30} + 56 q^{31} - q^{32} + 32 q^{33} - 18 q^{34} + 40 q^{35} - q^{36} + 138 q^{37} - 20 q^{38} + 74 q^{39} - 6 q^{40} + 46 q^{41} - 8 q^{42} + 132 q^{43} - 12 q^{44} - 6 q^{45} + 128 q^{47} - q^{48} + 207 q^{49} - 31 q^{50} + 70 q^{51} - 14 q^{52} + 34 q^{53} - 45 q^{54} + 104 q^{55} - 8 q^{56} - 64 q^{57} - 30 q^{58} + 28 q^{59} - 50 q^{60} - 62 q^{61} - 32 q^{62} - 228 q^{63} - q^{64} - 84 q^{65} - 188 q^{66} - 68 q^{67} - 18 q^{68} - 110 q^{69} - 48 q^{70} - 72 q^{71} - 89 q^{72} - 74 q^{73} - 38 q^{74} - 295 q^{75} - 20 q^{76} - 96 q^{77} - 146 q^{78} + 8 q^{79} - 6 q^{80} - 89 q^{81} - 42 q^{82} + 4 q^{83} - 52 q^{84} - 20 q^{85} - 44 q^{86} + 102 q^{87} - 12 q^{88} - 2 q^{89} - 6 q^{90} + 64 q^{91} - 32 q^{93} - 48 q^{94} + 144 q^{95} - q^{96} + 254 q^{97} + 119 q^{98} + 208 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3174))$$

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
3174.2.a $$\chi_{3174}(1, \cdot)$$ 3174.2.a.a 1 1
3174.2.a.b 1
3174.2.a.c 1
3174.2.a.d 1
3174.2.a.e 1
3174.2.a.f 1
3174.2.a.g 1
3174.2.a.h 2
3174.2.a.i 2
3174.2.a.j 2
3174.2.a.k 2
3174.2.a.l 2
3174.2.a.m 2
3174.2.a.n 2
3174.2.a.o 2
3174.2.a.p 2
3174.2.a.q 2
3174.2.a.r 2
3174.2.a.s 2
3174.2.a.t 4
3174.2.a.u 4
3174.2.a.v 4
3174.2.a.w 5
3174.2.a.x 5
3174.2.a.y 5
3174.2.a.z 5
3174.2.a.ba 5
3174.2.a.bb 5
3174.2.a.bc 5
3174.2.a.bd 5
3174.2.d $$\chi_{3174}(3173, \cdot)$$ n/a 168 1
3174.2.e $$\chi_{3174}(487, \cdot)$$ n/a 840 10
3174.2.f $$\chi_{3174}(263, \cdot)$$ n/a 1680 10
3174.2.i $$\chi_{3174}(139, \cdot)$$ n/a 2024 22
3174.2.j $$\chi_{3174}(137, \cdot)$$ n/a 4048 22
3174.2.m $$\chi_{3174}(13, \cdot)$$ n/a 20240 220
3174.2.p $$\chi_{3174}(5, \cdot)$$ n/a 40480 220

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3174))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3174)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(529))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1058))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1587))$$$$^{\oplus 2}$$