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Properties

Label 304.10
Level 304
Weight 10
Dimension 14423
Nonzero newspaces 12
Sturm bound 57600
Trace bound 7

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Defining parameters

Level: \( N \) = \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(57600\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(304))\).

Total New Old
Modular forms 26172 14575 11597
Cusp forms 25668 14423 11245
Eisenstein series 504 152 352

Trace form

\( 14423 q - 32 q^{2} + 137 q^{3} - 372 q^{4} + 679 q^{5} + 4348 q^{6} - 2779 q^{7} + 1396 q^{8} - 11633 q^{9} + O(q^{10}) \) \( 14423 q - 32 q^{2} + 137 q^{3} - 372 q^{4} + 679 q^{5} + 4348 q^{6} - 2779 q^{7} + 1396 q^{8} - 11633 q^{9} - 9404 q^{10} - 109759 q^{11} - 434348 q^{12} + 86119 q^{13} + 267044 q^{14} - 930915 q^{15} + 1634476 q^{16} - 344281 q^{17} - 4359840 q^{18} + 777199 q^{19} + 6555904 q^{20} + 594763 q^{21} + 68564 q^{22} - 2699355 q^{23} - 3727748 q^{24} + 60927 q^{25} + 12695500 q^{26} - 2718667 q^{27} - 7259092 q^{28} - 2181033 q^{29} + 9355572 q^{30} - 5338875 q^{31} + 3311948 q^{32} + 7057975 q^{33} + 9056372 q^{34} + 9687149 q^{35} - 47128316 q^{36} - 388082 q^{37} + 14996316 q^{38} - 92859254 q^{39} + 23502540 q^{40} - 9595737 q^{41} - 210798356 q^{42} + 227358513 q^{43} + 188446676 q^{44} + 5960799 q^{45} - 30864828 q^{46} - 473932475 q^{47} - 15663092 q^{48} + 246796571 q^{49} + 12579024 q^{50} + 460058141 q^{51} + 56568820 q^{52} + 169873079 q^{53} - 210622052 q^{54} - 433787099 q^{55} - 53022548 q^{56} - 25903945 q^{57} + 356543496 q^{58} + 259387857 q^{59} - 458068260 q^{60} + 1142548483 q^{61} + 273577852 q^{62} - 521628459 q^{63} + 698585820 q^{64} - 1578280961 q^{65} - 384547724 q^{66} - 9065107 q^{67} + 571514940 q^{68} + 712950627 q^{69} - 1212102436 q^{70} + 859556079 q^{71} - 1764151404 q^{72} - 1489608357 q^{73} - 247821756 q^{74} - 2461599324 q^{75} + 453269064 q^{76} - 2306375150 q^{77} + 3470049572 q^{78} - 855053657 q^{79} + 1400545676 q^{80} + 6691016007 q^{81} + 1348575132 q^{82} + 3417491059 q^{83} - 2563839860 q^{84} - 3337686557 q^{85} - 487961388 q^{86} - 5246494407 q^{87} - 3562294292 q^{88} - 3327500385 q^{89} - 6168174420 q^{90} + 591503765 q^{91} + 6263268972 q^{92} + 1097408687 q^{93} + 4136920508 q^{94} + 7241383761 q^{95} + 7792966232 q^{96} + 1456363687 q^{97} + 6201264168 q^{98} - 13045303991 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(304))\)

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
304.10.a \(\chi_{304}(1, \cdot)\) 304.10.a.a 1 1
304.10.a.b 1
304.10.a.c 3
304.10.a.d 4
304.10.a.e 4
304.10.a.f 6
304.10.a.g 6
304.10.a.h 7
304.10.a.i 8
304.10.a.j 9
304.10.a.k 10
304.10.a.l 10
304.10.a.m 12
304.10.b \(\chi_{304}(151, \cdot)\) None 0 1
304.10.c \(\chi_{304}(153, \cdot)\) None 0 1
304.10.h \(\chi_{304}(303, \cdot)\) 304.10.h.a 2 1
304.10.h.b 4
304.10.h.c 28
304.10.h.d 56
304.10.i \(\chi_{304}(49, \cdot)\) n/a 178 2
304.10.k \(\chi_{304}(77, \cdot)\) n/a 648 2
304.10.m \(\chi_{304}(75, \cdot)\) n/a 716 2
304.10.n \(\chi_{304}(31, \cdot)\) n/a 180 2
304.10.s \(\chi_{304}(103, \cdot)\) None 0 2
304.10.t \(\chi_{304}(121, \cdot)\) None 0 2
304.10.u \(\chi_{304}(17, \cdot)\) n/a 534 6
304.10.v \(\chi_{304}(45, \cdot)\) n/a 1432 4
304.10.x \(\chi_{304}(27, \cdot)\) n/a 1432 4
304.10.bb \(\chi_{304}(9, \cdot)\) None 0 6
304.10.bd \(\chi_{304}(71, \cdot)\) None 0 6
304.10.be \(\chi_{304}(15, \cdot)\) n/a 540 6
304.10.bg \(\chi_{304}(3, \cdot)\) n/a 4296 12
304.10.bi \(\chi_{304}(5, \cdot)\) n/a 4296 12

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)