## Defining parameters

 Level: $$N$$ = $$46 = 2 \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$6$$ Sturm bound: $$528$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(46))$$.

Total New Old
Modular forms 220 66 154
Cusp forms 176 66 110
Eisenstein series 44 0 44

## Trace form

 $$66 q + O(q^{10})$$ $$66 q + 748 q^{15} + 176 q^{17} - 88 q^{18} - 220 q^{19} - 352 q^{20} - 1320 q^{21} - 484 q^{22} - 968 q^{23} - 704 q^{25} - 220 q^{26} - 132 q^{27} + 176 q^{28} + 440 q^{29} + 1496 q^{30} + 1100 q^{31} + 1936 q^{33} + 1430 q^{35} + 1188 q^{37} - 132 q^{39} - 550 q^{41} - 1716 q^{43} - 2970 q^{45} - 1892 q^{47} - 2178 q^{49} - 660 q^{51} + 242 q^{53} + 3124 q^{54} + 6996 q^{55} + 1936 q^{56} + 8052 q^{57} + 1848 q^{58} + 4950 q^{59} + 88 q^{60} - 1056 q^{61} - 1716 q^{62} - 4180 q^{63} - 8624 q^{65} - 5456 q^{66} - 2904 q^{67} - 2992 q^{68} - 7480 q^{69} - 5808 q^{70} - 6820 q^{71} - 2464 q^{72} - 2112 q^{73} - 3344 q^{74} - 22 q^{75} + 440 q^{77} + 1452 q^{78} + 5126 q^{79} + 1408 q^{80} + 8580 q^{81} + 5016 q^{82} + 8954 q^{83} + 3784 q^{84} + 7898 q^{85} + 5236 q^{86} - 4686 q^{87} - 1870 q^{89} - 4004 q^{91} + 2376 q^{95} + 11330 q^{97} + 6952 q^{98} + 11550 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(46))$$

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
46.4.a $$\chi_{46}(1, \cdot)$$ 46.4.a.a 1 1
46.4.a.b 1
46.4.a.c 2
46.4.a.d 2
46.4.c $$\chi_{46}(3, \cdot)$$ 46.4.c.a 30 10
46.4.c.b 30

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(46))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(46)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$