# Properties

 Label 387.8 Level 387 Weight 8 Dimension 30504 Nonzero newspaces 20 Sturm bound 88704 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$387 = 3^{2} \cdot 43$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$20$$ Sturm bound: $$88704$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(387))$$.

Total New Old
Modular forms 39144 30872 8272
Cusp forms 38472 30504 7968
Eisenstein series 672 368 304

## Trace form

 $$30504q - 33q^{2} - 132q^{3} - 165q^{4} + 1077q^{5} + 2382q^{6} - 807q^{7} - 14547q^{8} - 2064q^{9} + O(q^{10})$$ $$30504q - 33q^{2} - 132q^{3} - 165q^{4} + 1077q^{5} + 2382q^{6} - 807q^{7} - 14547q^{8} - 2064q^{9} + 17667q^{10} + 14961q^{11} - 16188q^{12} - 13731q^{13} + 31713q^{14} + 2292q^{15} - 13917q^{16} - 4419q^{17} - 85836q^{18} - 164517q^{19} + 9753q^{20} + 374364q^{21} + 542115q^{22} + 72537q^{23} - 431022q^{24} - 213645q^{25} - 1134183q^{26} - 644628q^{27} - 404277q^{28} + 902253q^{29} + 2224140q^{30} - 659578q^{31} + 3253539q^{32} + 296952q^{33} - 61281q^{34} - 5090673q^{35} - 5003706q^{36} - 1590123q^{37} + 508395q^{38} + 4114548q^{39} + 7642353q^{40} + 3443484q^{41} - 1077816q^{42} + 6096348q^{43} - 6621138q^{44} - 5375244q^{45} - 3130221q^{46} + 2407680q^{47} + 14868966q^{48} - 744178q^{49} - 1947537q^{50} - 5051460q^{51} + 4544093q^{52} + 2622099q^{53} - 11633142q^{54} - 1288815q^{55} - 8247963q^{56} + 6143616q^{57} + 11941785q^{58} + 6723969q^{59} - 743052q^{60} + 8800437q^{61} - 1268103q^{62} + 4477524q^{63} - 3691713q^{64} - 1201263q^{65} - 11509608q^{66} - 22028127q^{67} - 9508365q^{68} + 6004500q^{69} + 9097473q^{70} + 28893639q^{71} + 19276566q^{72} + 42052185q^{73} - 5407980q^{74} - 38349348q^{75} - 78661704q^{76} - 70515129q^{77} + 26679840q^{78} - 41752443q^{79} + 43263513q^{80} + 57077376q^{81} + 28426953q^{82} + 6730605q^{83} - 60174888q^{84} + 61596504q^{85} + 69310320q^{86} - 20581584q^{87} + 128434563q^{88} + 36771513q^{89} + 27321108q^{90} - 76295025q^{91} - 227286429q^{92} - 54662508q^{93} - 228280935q^{94} - 95408307q^{95} + 6808668q^{96} + 31167471q^{97} + 236343300q^{98} + 98765268q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(387))$$

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
387.8.a $$\chi_{387}(1, \cdot)$$ 387.8.a.a 10 1
387.8.a.b 11
387.8.a.c 12
387.8.a.d 13
387.8.a.e 13
387.8.a.f 15
387.8.a.g 22
387.8.a.h 26
387.8.d $$\chi_{387}(386, \cdot)$$ n/a 104 1
387.8.e $$\chi_{387}(49, \cdot)$$ n/a 612 2
387.8.f $$\chi_{387}(130, \cdot)$$ n/a 588 2
387.8.g $$\chi_{387}(178, \cdot)$$ n/a 612 2
387.8.h $$\chi_{387}(208, \cdot)$$ n/a 254 2
387.8.k $$\chi_{387}(308, \cdot)$$ n/a 612 2
387.8.l $$\chi_{387}(128, \cdot)$$ n/a 612 2
387.8.m $$\chi_{387}(50, \cdot)$$ n/a 612 2
387.8.t $$\chi_{387}(80, \cdot)$$ n/a 204 2
387.8.u $$\chi_{387}(64, \cdot)$$ n/a 768 6
387.8.v $$\chi_{387}(8, \cdot)$$ n/a 624 6
387.8.y $$\chi_{387}(10, \cdot)$$ n/a 1524 12
387.8.z $$\chi_{387}(13, \cdot)$$ n/a 3672 12
387.8.ba $$\chi_{387}(4, \cdot)$$ n/a 3672 12
387.8.bb $$\chi_{387}(25, \cdot)$$ n/a 3672 12
387.8.bc $$\chi_{387}(26, \cdot)$$ n/a 1224 12
387.8.bj $$\chi_{387}(20, \cdot)$$ n/a 3672 12
387.8.bk $$\chi_{387}(2, \cdot)$$ n/a 3672 12
387.8.bl $$\chi_{387}(5, \cdot)$$ n/a 3672 12

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

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(387))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(387)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(129))$$$$^{\oplus 2}$$