# Properties

 Label 12.7 Level 12 Weight 7 Dimension 8 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 56 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(12))$$.

Total New Old
Modular forms 29 8 21
Cusp forms 19 8 11
Eisenstein series 10 0 10

## Trace form

 $$8q - 10q^{2} - 6q^{3} + 156q^{4} - 44q^{5} - 162q^{6} + 484q^{7} + 1136q^{8} - 2880q^{9} + O(q^{10})$$ $$8q - 10q^{2} - 6q^{3} + 156q^{4} - 44q^{5} - 162q^{6} + 484q^{7} + 1136q^{8} - 2880q^{9} + 84q^{10} - 972q^{12} + 1888q^{13} + 4776q^{14} - 8640q^{15} - 9744q^{16} + 12220q^{17} + 2430q^{18} + 11572q^{19} + 17608q^{20} - 11172q^{21} - 13512q^{22} - 7776q^{24} + 35828q^{25} - 59252q^{26} + 12906q^{27} - 17808q^{28} - 84860q^{29} + 57348q^{30} - 40892q^{31} + 61280q^{32} + 99576q^{33} + 109404q^{34} - 37908q^{36} - 72752q^{37} - 128088q^{38} - 15708q^{39} - 195552q^{40} - 65252q^{41} + 210600q^{42} + 137236q^{43} + 445008q^{44} + 62532q^{45} + 81120q^{46} - 276048q^{48} - 229716q^{49} - 743118q^{50} - 380160q^{51} - 179592q^{52} + 470308q^{53} + 39366q^{54} + 570240q^{55} + 793728q^{56} - 238836q^{57} + 529860q^{58} - 723816q^{60} + 62512q^{61} - 513384q^{62} - 344124q^{63} - 642432q^{64} + 321512q^{65} + 771768q^{66} - 168716q^{67} + 690328q^{68} + 1042848q^{69} + 938928q^{70} - 276048q^{72} - 1511024q^{73} - 1522916q^{74} + 61770q^{75} + 67824q^{76} - 1487328q^{77} + 396252q^{78} - 319484q^{79} + 1272352q^{80} + 1313496q^{81} + 240444q^{82} - 143856q^{84} - 1466040q^{85} - 1154568q^{86} + 665280q^{87} + 489600q^{88} + 730924q^{89} - 20412q^{90} + 1267112q^{91} - 1338816q^{92} + 39084q^{93} - 390288q^{94} + 624672q^{96} + 5048464q^{97} + 1604918q^{98} - 570240q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(12))$$

We only show spaces with odd 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
12.7.c $$\chi_{12}(5, \cdot)$$ 12.7.c.a 2 1
12.7.d $$\chi_{12}(7, \cdot)$$ 12.7.d.a 6 1

## Decomposition of $$S_{7}^{\mathrm{old}}(\Gamma_1(12))$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(\Gamma_1(12)) \cong$$ $$S_{7}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$