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Properties

Label 495.4
Level 495
Weight 4
Dimension 18254
Nonzero newspaces 24
Sturm bound 69120
Trace bound 5

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Defining parameters

Level: \( N \) = \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(69120\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(495))\).

Total New Old
Modular forms 26560 18742 7818
Cusp forms 25280 18254 7026
Eisenstein series 1280 488 792

Trace form

\( 18254 q - 26 q^{2} - 36 q^{3} - 90 q^{4} - 57 q^{5} - 52 q^{6} + 38 q^{7} + 34 q^{8} + 28 q^{9} + O(q^{10}) \) \( 18254 q - 26 q^{2} - 36 q^{3} - 90 q^{4} - 57 q^{5} - 52 q^{6} + 38 q^{7} + 34 q^{8} + 28 q^{9} - 406 q^{10} - 314 q^{11} - 432 q^{12} + 162 q^{13} + 1056 q^{14} + 346 q^{15} + 1866 q^{16} + 1402 q^{17} + 840 q^{18} - 1292 q^{19} - 2576 q^{20} - 1140 q^{21} - 2628 q^{22} - 3908 q^{23} - 3388 q^{24} - 169 q^{25} - 1564 q^{26} - 528 q^{27} + 7072 q^{28} + 5550 q^{29} + 4412 q^{30} + 6110 q^{31} + 13692 q^{32} + 4676 q^{33} + 4544 q^{34} + 3573 q^{35} + 3668 q^{36} - 2174 q^{37} - 2308 q^{38} - 660 q^{39} - 8802 q^{40} - 10786 q^{41} - 13576 q^{42} - 9944 q^{43} - 18236 q^{44} - 7214 q^{45} - 6076 q^{46} - 9618 q^{47} - 10876 q^{48} - 836 q^{49} - 2080 q^{50} - 2760 q^{51} - 2940 q^{52} - 3234 q^{53} + 1548 q^{54} + 4527 q^{55} + 13456 q^{56} + 4436 q^{57} + 15616 q^{58} + 11620 q^{59} + 10968 q^{60} + 7838 q^{61} + 31196 q^{62} + 14020 q^{63} + 17718 q^{64} + 9646 q^{65} + 15864 q^{66} + 6100 q^{67} + 18024 q^{68} + 12004 q^{69} - 946 q^{70} + 20882 q^{71} + 18488 q^{72} - 770 q^{73} + 1220 q^{74} + 7790 q^{75} - 7964 q^{76} - 13116 q^{77} - 10112 q^{78} - 10338 q^{79} - 7966 q^{80} + 668 q^{81} - 27930 q^{82} - 9544 q^{83} + 9812 q^{84} - 1741 q^{85} - 20530 q^{86} - 15460 q^{87} - 21732 q^{88} - 37916 q^{89} - 48564 q^{90} - 25774 q^{91} - 64480 q^{92} - 33188 q^{93} - 7552 q^{94} - 20301 q^{95} - 68596 q^{96} - 424 q^{97} - 28588 q^{98} - 31266 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.4.a \(\chi_{495}(1, \cdot)\) 495.4.a.a 1 1
495.4.a.b 1
495.4.a.c 1
495.4.a.d 2
495.4.a.e 2
495.4.a.f 3
495.4.a.g 3
495.4.a.h 3
495.4.a.i 3
495.4.a.j 3
495.4.a.k 3
495.4.a.l 3
495.4.a.m 4
495.4.a.n 4
495.4.a.o 7
495.4.a.p 7
495.4.c \(\chi_{495}(199, \cdot)\) 495.4.c.a 6 1
495.4.c.b 10
495.4.c.c 14
495.4.c.d 14
495.4.c.e 16
495.4.c.f 16
495.4.d \(\chi_{495}(494, \cdot)\) 495.4.d.a 16 1
495.4.d.b 56
495.4.f \(\chi_{495}(296, \cdot)\) 495.4.f.a 48 1
495.4.i \(\chi_{495}(166, \cdot)\) n/a 240 2
495.4.k \(\chi_{495}(208, \cdot)\) n/a 176 2
495.4.l \(\chi_{495}(188, \cdot)\) n/a 120 2
495.4.n \(\chi_{495}(91, \cdot)\) n/a 240 4
495.4.p \(\chi_{495}(131, \cdot)\) n/a 288 2
495.4.r \(\chi_{495}(164, \cdot)\) n/a 424 2
495.4.u \(\chi_{495}(34, \cdot)\) n/a 360 2
495.4.x \(\chi_{495}(116, \cdot)\) n/a 192 4
495.4.z \(\chi_{495}(134, \cdot)\) n/a 288 4
495.4.ba \(\chi_{495}(64, \cdot)\) n/a 352 4
495.4.bc \(\chi_{495}(23, \cdot)\) n/a 720 4
495.4.bf \(\chi_{495}(43, \cdot)\) n/a 848 4
495.4.bg \(\chi_{495}(16, \cdot)\) n/a 1152 8
495.4.bi \(\chi_{495}(53, \cdot)\) n/a 576 8
495.4.bj \(\chi_{495}(28, \cdot)\) n/a 704 8
495.4.bl \(\chi_{495}(4, \cdot)\) n/a 1696 8
495.4.bo \(\chi_{495}(29, \cdot)\) n/a 1696 8
495.4.bq \(\chi_{495}(41, \cdot)\) n/a 1152 8
495.4.bs \(\chi_{495}(7, \cdot)\) n/a 3392 16
495.4.bv \(\chi_{495}(38, \cdot)\) n/a 3392 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(495)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)