Properties

Label 2023.4
Level 2023
Weight 4
Dimension 473435
Nonzero newspaces 20
Sturm bound 1331712
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1331712\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2023))\).

Total New Old
Modular forms 501792 477119 24673
Cusp forms 496992 473435 23557
Eisenstein series 4800 3684 1116

Trace form

\( 473435q - 483q^{2} - 489q^{3} - 483q^{4} - 471q^{5} - 450q^{6} - 579q^{7} - 1233q^{8} - 525q^{9} + O(q^{10}) \) \( 473435q - 483q^{2} - 489q^{3} - 483q^{4} - 471q^{5} - 450q^{6} - 579q^{7} - 1233q^{8} - 525q^{9} - 926q^{10} - 931q^{11} - 822q^{12} - 352q^{13} - 259q^{14} + 210q^{15} + 1337q^{16} - 256q^{17} + 843q^{18} - 319q^{19} - 200q^{20} - 1023q^{21} - 2108q^{22} - 1105q^{23} - 7830q^{24} - 5185q^{25} - 4608q^{26} - 1314q^{27} - 123q^{28} - 154q^{29} + 4830q^{30} + 2841q^{31} + 3903q^{32} + 3763q^{33} + 3712q^{34} + 761q^{35} + 5441q^{36} + 1743q^{37} - 1780q^{38} - 5302q^{39} - 10056q^{40} - 5278q^{41} - 6078q^{42} - 7176q^{43} - 8252q^{44} - 6362q^{45} - 4242q^{46} + 5399q^{47} + 12430q^{48} + 2619q^{49} + 9533q^{50} + 2688q^{51} + 11108q^{52} - 2177q^{53} - 11262q^{54} - 8230q^{55} - 3377q^{56} - 8646q^{57} - 6406q^{58} - 3021q^{59} - 5724q^{60} + 405q^{61} - 7360q^{62} + 3651q^{63} - 8855q^{64} + 4466q^{65} + 20278q^{66} + 7893q^{67} + 6768q^{68} + 11726q^{69} + 1566q^{70} - 2064q^{71} - 73q^{72} + 1131q^{73} + 384q^{74} + 3246q^{75} + 1850q^{76} - 785q^{77} - 8672q^{78} - 1345q^{79} - 3168q^{80} - 11156q^{81} - 3026q^{82} - 21582q^{83} - 17582q^{84} - 9896q^{85} - 34792q^{86} - 6618q^{87} + 6192q^{88} - 3837q^{89} - 3688q^{90} + 1692q^{91} + 13624q^{92} + 7427q^{93} + 13890q^{94} + 12969q^{95} + 43426q^{96} - 798q^{97} + 23069q^{98} + 38636q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2023))\)

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
2023.4.a \(\chi_{2023}(1, \cdot)\) 2023.4.a.a 1 1
2023.4.a.b 1
2023.4.a.c 1
2023.4.a.d 1
2023.4.a.e 3
2023.4.a.f 4
2023.4.a.g 7
2023.4.a.h 9
2023.4.a.i 11
2023.4.a.j 11
2023.4.a.k 12
2023.4.a.l 12
2023.4.a.m 13
2023.4.a.n 13
2023.4.a.o 26
2023.4.a.p 26
2023.4.a.q 33
2023.4.a.r 33
2023.4.a.s 39
2023.4.a.t 39
2023.4.a.u 56
2023.4.a.v 56
2023.4.b \(\chi_{2023}(288, \cdot)\) n/a 406 1
2023.4.e \(\chi_{2023}(1157, \cdot)\) n/a 1054 2
2023.4.g \(\chi_{2023}(540, \cdot)\) n/a 812 2
2023.4.j \(\chi_{2023}(1444, \cdot)\) n/a 1052 2
2023.4.k \(\chi_{2023}(134, \cdot)\) n/a 1616 4
2023.4.n \(\chi_{2023}(905, \cdot)\) n/a 2104 4
2023.4.p \(\chi_{2023}(447, \cdot)\) n/a 4208 8
2023.4.q \(\chi_{2023}(120, \cdot)\) n/a 7328 16
2023.4.r \(\chi_{2023}(179, \cdot)\) n/a 4208 8
2023.4.v \(\chi_{2023}(50, \cdot)\) n/a 7328 16
2023.4.w \(\chi_{2023}(40, \cdot)\) n/a 8416 16
2023.4.y \(\chi_{2023}(18, \cdot)\) n/a 19520 32
2023.4.z \(\chi_{2023}(64, \cdot)\) n/a 14656 32
2023.4.bb \(\chi_{2023}(16, \cdot)\) n/a 19520 32
2023.4.bf \(\chi_{2023}(8, \cdot)\) n/a 29440 64
2023.4.bg \(\chi_{2023}(4, \cdot)\) n/a 39040 64
2023.4.bi \(\chi_{2023}(6, \cdot)\) n/a 78080 128
2023.4.bl \(\chi_{2023}(2, \cdot)\) n/a 78080 128
2023.4.bn \(\chi_{2023}(3, \cdot)\) n/a 156160 256

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2023))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2023)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)