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Properties

Label 588.5
Level 588
Weight 5
Dimension 15701
Nonzero newspaces 16
Sturm bound 94080
Trace bound 3

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Defining parameters

Level: \( N \) = \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(94080\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(588))\).

Total New Old
Modular forms 38232 15893 22339
Cusp forms 37032 15701 21331
Eisenstein series 1200 192 1008

Trace form

\( 15701 q + 6 q^{2} + 27 q^{3} - 50 q^{4} - 84 q^{5} - 39 q^{6} + 104 q^{7} - 540 q^{8} + 93 q^{9} + O(q^{10}) \) \( 15701 q + 6 q^{2} + 27 q^{3} - 50 q^{4} - 84 q^{5} - 39 q^{6} + 104 q^{7} - 540 q^{8} + 93 q^{9} + 986 q^{10} + 684 q^{11} + 855 q^{12} - 286 q^{13} - 648 q^{14} - 948 q^{15} - 3230 q^{16} - 2328 q^{17} - 1827 q^{18} - 1998 q^{19} + 3168 q^{20} + 1155 q^{21} - 2886 q^{22} + 2880 q^{23} - 2445 q^{24} + 11509 q^{25} - 1368 q^{26} - 531 q^{27} + 2604 q^{28} - 13440 q^{29} + 9195 q^{30} - 9510 q^{31} + 8916 q^{32} - 8124 q^{33} + 9050 q^{34} + 666 q^{35} - 14559 q^{36} - 5630 q^{37} - 13140 q^{38} + 6159 q^{39} - 5866 q^{40} + 19956 q^{41} + 6609 q^{42} + 6406 q^{43} + 13728 q^{44} + 15882 q^{45} - 6354 q^{46} - 6120 q^{47} + 1008 q^{48} - 24042 q^{49} - 32538 q^{50} - 19782 q^{51} - 27874 q^{52} - 24084 q^{53} - 32403 q^{54} - 77574 q^{55} - 13122 q^{56} + 8310 q^{57} + 21338 q^{58} + 10620 q^{59} + 56259 q^{60} + 115116 q^{61} + 106176 q^{62} + 14556 q^{63} + 94918 q^{64} + 18276 q^{65} + 30375 q^{66} - 6742 q^{67} - 2424 q^{68} - 27726 q^{69} - 43146 q^{70} - 41328 q^{71} - 22473 q^{72} - 64654 q^{73} - 85296 q^{74} - 35967 q^{75} - 105738 q^{76} - 19656 q^{77} + 24069 q^{78} - 24718 q^{79} + 176670 q^{80} + 89397 q^{81} + 148952 q^{82} + 70560 q^{83} + 14058 q^{84} + 19468 q^{85} - 41898 q^{86} - 69168 q^{87} - 241668 q^{88} - 140208 q^{89} - 361260 q^{90} - 133048 q^{91} - 31458 q^{92} - 13902 q^{93} - 26628 q^{94} - 88668 q^{95} - 52488 q^{96} + 81122 q^{97} + 83538 q^{98} + 84348 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(588))\)

We only show spaces with odd 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
588.5.c \(\chi_{588}(197, \cdot)\) 588.5.c.a 1 1
588.5.c.b 1
588.5.c.c 1
588.5.c.d 8
588.5.c.e 8
588.5.c.f 10
588.5.c.g 10
588.5.c.h 16
588.5.d \(\chi_{588}(97, \cdot)\) 588.5.d.a 4 1
588.5.d.b 6
588.5.d.c 16
588.5.g \(\chi_{588}(295, \cdot)\) n/a 164 1
588.5.h \(\chi_{588}(587, \cdot)\) n/a 312 1
588.5.j \(\chi_{588}(215, \cdot)\) n/a 624 2
588.5.l \(\chi_{588}(67, \cdot)\) n/a 320 2
588.5.m \(\chi_{588}(313, \cdot)\) 588.5.m.a 4 2
588.5.m.b 6
588.5.m.c 6
588.5.m.d 6
588.5.m.e 16
588.5.m.f 16
588.5.p \(\chi_{588}(557, \cdot)\) n/a 106 2
588.5.r \(\chi_{588}(83, \cdot)\) n/a 2664 6
588.5.s \(\chi_{588}(43, \cdot)\) n/a 1344 6
588.5.v \(\chi_{588}(13, \cdot)\) n/a 228 6
588.5.w \(\chi_{588}(29, \cdot)\) n/a 444 6
588.5.z \(\chi_{588}(53, \cdot)\) n/a 900 12
588.5.bc \(\chi_{588}(61, \cdot)\) n/a 444 12
588.5.bd \(\chi_{588}(151, \cdot)\) n/a 2688 12
588.5.bf \(\chi_{588}(47, \cdot)\) n/a 5328 12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(588))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(588)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)