Properties

Label 605.6
Level 605
Weight 6
Dimension 65033
Nonzero newspaces 12
Sturm bound 174240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(174240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(605))\).

Total New Old
Modular forms 73240 65875 7365
Cusp forms 71960 65033 6927
Eisenstein series 1280 842 438

Trace form

\( 65033 q - 88 q^{2} - 94 q^{3} - 142 q^{4} - 200 q^{5} - 94 q^{6} + 1282 q^{7} + 430 q^{8} - 2823 q^{9} + O(q^{10}) \) \( 65033 q - 88 q^{2} - 94 q^{3} - 142 q^{4} - 200 q^{5} - 94 q^{6} + 1282 q^{7} + 430 q^{8} - 2823 q^{9} - 2535 q^{10} - 1190 q^{11} - 1338 q^{12} + 2216 q^{13} - 894 q^{14} + 8565 q^{15} + 30418 q^{16} + 5252 q^{17} - 11724 q^{18} - 8410 q^{19} - 17125 q^{20} - 38714 q^{21} - 25240 q^{22} - 37974 q^{23} + 110 q^{24} + 28080 q^{25} + 133666 q^{26} + 95510 q^{27} + 124114 q^{28} - 460 q^{29} - 54845 q^{30} - 90414 q^{31} - 300278 q^{32} - 85320 q^{33} - 11894 q^{34} + 46535 q^{35} + 284738 q^{36} + 137812 q^{37} + 243810 q^{38} + 117874 q^{39} + 95755 q^{40} - 51404 q^{41} - 121726 q^{42} - 149274 q^{43} - 286930 q^{44} - 431380 q^{45} - 370554 q^{46} - 166838 q^{47} - 129014 q^{48} + 172953 q^{49} + 254865 q^{50} + 358006 q^{51} + 272282 q^{52} + 378176 q^{53} + 1148410 q^{54} + 240990 q^{55} + 906890 q^{56} + 225850 q^{57} + 271830 q^{58} + 134730 q^{59} - 463845 q^{60} - 554304 q^{61} - 1229566 q^{62} - 1078414 q^{63} - 1565962 q^{64} - 606815 q^{65} - 242250 q^{66} - 377258 q^{67} + 65114 q^{68} + 457774 q^{69} + 855155 q^{70} - 382494 q^{71} - 114690 q^{72} + 23556 q^{73} + 1459326 q^{74} + 67105 q^{75} + 1114830 q^{76} + 787110 q^{77} + 1665662 q^{78} + 928850 q^{79} - 395765 q^{80} - 1700967 q^{81} - 2280926 q^{82} - 1154034 q^{83} + 387146 q^{84} - 102635 q^{85} + 1131186 q^{86} + 71170 q^{87} + 240700 q^{88} + 317080 q^{89} + 1927545 q^{90} + 506566 q^{91} + 542682 q^{92} - 557458 q^{93} - 1637214 q^{94} - 1340105 q^{95} - 4971834 q^{96} - 697728 q^{97} - 1688716 q^{98} - 527300 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(605))\)

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
605.6.a \(\chi_{605}(1, \cdot)\) 605.6.a.a 1 1
605.6.a.b 3
605.6.a.c 4
605.6.a.d 5
605.6.a.e 6
605.6.a.f 7
605.6.a.g 7
605.6.a.h 8
605.6.a.i 9
605.6.a.j 9
605.6.a.k 10
605.6.a.l 14
605.6.a.m 18
605.6.a.n 20
605.6.a.o 20
605.6.a.p 20
605.6.a.q 20
605.6.b \(\chi_{605}(364, \cdot)\) n/a 264 1
605.6.e \(\chi_{605}(362, \cdot)\) n/a 524 2
605.6.g \(\chi_{605}(81, \cdot)\) n/a 720 4
605.6.j \(\chi_{605}(9, \cdot)\) n/a 1048 4
605.6.k \(\chi_{605}(56, \cdot)\) n/a 2200 10
605.6.m \(\chi_{605}(112, \cdot)\) n/a 2096 8
605.6.o \(\chi_{605}(34, \cdot)\) n/a 3280 10
605.6.r \(\chi_{605}(32, \cdot)\) n/a 6560 20
605.6.s \(\chi_{605}(16, \cdot)\) n/a 8800 40
605.6.u \(\chi_{605}(4, \cdot)\) n/a 13120 40
605.6.w \(\chi_{605}(2, \cdot)\) n/a 26240 80

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(605)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)