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Properties

Label 605.4
Level 605
Weight 4
Dimension 38851
Nonzero newspaces 12
Sturm bound 116160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(116160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(605))\).

Total New Old
Modular forms 44200 39693 4507
Cusp forms 42920 38851 4069
Eisenstein series 1280 842 438

Trace form

\( 38851 q - 94 q^{2} - 88 q^{3} - 82 q^{4} - 140 q^{5} - 478 q^{6} - 124 q^{7} + 70 q^{8} + 207 q^{9} + O(q^{10}) \) \( 38851 q - 94 q^{2} - 88 q^{3} - 82 q^{4} - 140 q^{5} - 478 q^{6} - 124 q^{7} + 70 q^{8} + 207 q^{9} + 75 q^{10} - 200 q^{11} + 486 q^{12} - 48 q^{13} - 894 q^{14} - 765 q^{15} - 1854 q^{16} - 664 q^{17} - 18 q^{18} + 910 q^{19} + 695 q^{20} + 1402 q^{21} + 1160 q^{22} - 648 q^{23} - 850 q^{24} - 230 q^{25} - 818 q^{26} - 610 q^{27} - 702 q^{28} - 340 q^{29} - 845 q^{30} - 1938 q^{31} + 1066 q^{32} - 510 q^{33} - 1634 q^{34} - 25 q^{35} - 274 q^{36} + 736 q^{37} + 1050 q^{38} + 2914 q^{39} + 2515 q^{40} + 1792 q^{41} + 8162 q^{42} + 3772 q^{43} + 2150 q^{44} + 5960 q^{45} + 6502 q^{46} + 1996 q^{47} + 1642 q^{48} - 1237 q^{49} - 4245 q^{50} - 8558 q^{51} - 20334 q^{52} - 14248 q^{53} - 29750 q^{54} - 6070 q^{55} - 22870 q^{56} - 13190 q^{57} - 8510 q^{58} + 1590 q^{59} - 4485 q^{60} - 1428 q^{61} + 11042 q^{62} + 4112 q^{63} + 13718 q^{64} + 8605 q^{65} + 8550 q^{66} + 15596 q^{67} + 26018 q^{68} + 15934 q^{69} + 15155 q^{70} + 2022 q^{71} + 9270 q^{72} - 11168 q^{73} - 7014 q^{74} - 185 q^{75} + 1310 q^{76} - 4560 q^{77} - 6946 q^{78} - 1650 q^{79} - 6725 q^{80} - 5109 q^{81} - 12098 q^{82} + 2292 q^{83} - 694 q^{84} + 5415 q^{85} + 1602 q^{86} + 13870 q^{87} + 9260 q^{88} + 7480 q^{89} + 28275 q^{90} + 23822 q^{91} + 28746 q^{92} + 27974 q^{93} + 37506 q^{94} + 18805 q^{95} + 42342 q^{96} + 14996 q^{97} + 18758 q^{98} + 3340 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(605))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
605.4.a \(\chi_{605}(1, \cdot)\) 605.4.a.a 1 1
605.4.a.b 1
605.4.a.c 1
605.4.a.d 1
605.4.a.e 2
605.4.a.f 2
605.4.a.g 2
605.4.a.h 3
605.4.a.i 4
605.4.a.j 4
605.4.a.k 4
605.4.a.l 4
605.4.a.m 6
605.4.a.n 6
605.4.a.o 8
605.4.a.p 12
605.4.a.q 12
605.4.a.r 12
605.4.a.s 12
605.4.a.t 12
605.4.b \(\chi_{605}(364, \cdot)\) n/a 154 1
605.4.e \(\chi_{605}(362, \cdot)\) n/a 308 2
605.4.g \(\chi_{605}(81, \cdot)\) n/a 432 4
605.4.j \(\chi_{605}(9, \cdot)\) n/a 616 4
605.4.k \(\chi_{605}(56, \cdot)\) n/a 1320 10
605.4.m \(\chi_{605}(112, \cdot)\) n/a 1232 8
605.4.o \(\chi_{605}(34, \cdot)\) n/a 1960 10
605.4.r \(\chi_{605}(32, \cdot)\) n/a 3920 20
605.4.s \(\chi_{605}(16, \cdot)\) n/a 5280 40
605.4.u \(\chi_{605}(4, \cdot)\) n/a 7840 40
605.4.w \(\chi_{605}(2, \cdot)\) n/a 15680 80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces

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