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Properties

Label 592.3
Level 592
Weight 3
Dimension 12136
Nonzero newspaces 21
Sturm bound 65664
Trace bound 13

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Defining parameters

Level: \( N \) = \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 21 \)
Sturm bound: \(65664\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(592))\).

Total New Old
Modular forms 22392 12452 9940
Cusp forms 21384 12136 9248
Eisenstein series 1008 316 692

Trace form

\( 12136 q - 68 q^{2} - 50 q^{3} - 56 q^{4} - 74 q^{5} - 56 q^{6} - 46 q^{7} - 80 q^{8} - 36 q^{9} + O(q^{10}) \) \( 12136 q - 68 q^{2} - 50 q^{3} - 56 q^{4} - 74 q^{5} - 56 q^{6} - 46 q^{7} - 80 q^{8} - 36 q^{9} - 144 q^{10} - 18 q^{11} - 176 q^{12} - 106 q^{13} - 96 q^{14} - 54 q^{15} + 8 q^{16} - 94 q^{17} + 76 q^{18} - 114 q^{19} + 96 q^{20} - 50 q^{21} + 32 q^{22} - 174 q^{23} - 168 q^{24} - 40 q^{25} - 264 q^{26} - 182 q^{27} - 184 q^{28} - 138 q^{29} - 176 q^{30} - 54 q^{31} - 88 q^{32} - 154 q^{33} + 80 q^{34} + 146 q^{35} + 32 q^{36} - 66 q^{37} - 224 q^{38} + 338 q^{39} - 152 q^{40} - 54 q^{41} - 24 q^{42} + 174 q^{43} - 112 q^{44} - 114 q^{45} - 128 q^{46} - 54 q^{47} - 24 q^{48} - 168 q^{49} - 164 q^{50} - 366 q^{51} - 272 q^{52} - 426 q^{53} - 136 q^{54} - 558 q^{55} + 264 q^{56} - 18 q^{57} + 280 q^{58} - 466 q^{59} + 248 q^{60} - 106 q^{61} + 216 q^{62} - 54 q^{63} - 200 q^{64} - 66 q^{65} - 464 q^{66} + 398 q^{67} - 296 q^{68} + 142 q^{69} - 40 q^{70} + 466 q^{71} - 176 q^{72} + 220 q^{73} + 20 q^{74} + 368 q^{75} + 304 q^{76} + 334 q^{77} + 96 q^{78} - 54 q^{79} - 536 q^{80} - 496 q^{81} - 680 q^{82} - 690 q^{83} - 536 q^{84} - 26 q^{85} - 608 q^{86} - 942 q^{87} - 56 q^{88} + 138 q^{89} + 248 q^{90} - 430 q^{91} + 264 q^{92} - 26 q^{93} - 168 q^{94} - 54 q^{95} + 88 q^{96} - 414 q^{97} - 92 q^{98} + 398 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(592))\)

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
592.3.b \(\chi_{592}(591, \cdot)\) 592.3.b.a 2 1
592.3.b.b 12
592.3.b.c 24
592.3.d \(\chi_{592}(223, \cdot)\) 592.3.d.a 12 1
592.3.d.b 24
592.3.f \(\chi_{592}(519, \cdot)\) None 0 1
592.3.h \(\chi_{592}(295, \cdot)\) None 0 1
592.3.k \(\chi_{592}(401, \cdot)\) 592.3.k.a 2 2
592.3.k.b 2
592.3.k.c 2
592.3.k.d 4
592.3.k.e 12
592.3.k.f 14
592.3.k.g 18
592.3.k.h 20
592.3.l \(\chi_{592}(117, \cdot)\) n/a 300 2
592.3.p \(\chi_{592}(75, \cdot)\) n/a 288 2
592.3.q \(\chi_{592}(147, \cdot)\) n/a 300 2
592.3.r \(\chi_{592}(413, \cdot)\) n/a 300 2
592.3.u \(\chi_{592}(105, \cdot)\) None 0 2
592.3.v \(\chi_{592}(455, \cdot)\) None 0 2
592.3.x \(\chi_{592}(343, \cdot)\) None 0 2
592.3.z \(\chi_{592}(47, \cdot)\) 592.3.z.a 4 2
592.3.z.b 24
592.3.z.c 24
592.3.z.d 24
592.3.bb \(\chi_{592}(159, \cdot)\) 592.3.bb.a 24 2
592.3.bb.b 24
592.3.bb.c 28
592.3.bd \(\chi_{592}(393, \cdot)\) None 0 4
592.3.bg \(\chi_{592}(45, \cdot)\) n/a 600 4
592.3.bh \(\chi_{592}(11, \cdot)\) n/a 600 4
592.3.bi \(\chi_{592}(195, \cdot)\) n/a 600 4
592.3.bm \(\chi_{592}(29, \cdot)\) n/a 600 4
592.3.bn \(\chi_{592}(97, \cdot)\) n/a 148 4
592.3.bp \(\chi_{592}(151, \cdot)\) None 0 6
592.3.br \(\chi_{592}(7, \cdot)\) None 0 6
592.3.bt \(\chi_{592}(95, \cdot)\) n/a 228 6
592.3.bu \(\chi_{592}(127, \cdot)\) n/a 228 6
592.3.bw \(\chi_{592}(57, \cdot)\) None 0 12
592.3.bz \(\chi_{592}(83, \cdot)\) n/a 1800 12
592.3.cb \(\chi_{592}(13, \cdot)\) n/a 1800 12
592.3.cc \(\chi_{592}(5, \cdot)\) n/a 1800 12
592.3.cf \(\chi_{592}(3, \cdot)\) n/a 1800 12
592.3.cg \(\chi_{592}(17, \cdot)\) n/a 444 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(592))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(592)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 2}\)