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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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