Properties

Label 1452.4
Level 1452
Weight 4
Dimension 74695
Nonzero newspaces 16
Sturm bound 464640
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(464640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1452))\).

Total New Old
Modular forms 175840 75259 100581
Cusp forms 172640 74695 97945
Eisenstein series 3200 564 2636

Trace form

\( 74695 q + 3 q^{3} - 98 q^{4} - 18 q^{5} - 69 q^{6} - 32 q^{7} + 67 q^{9} + O(q^{10}) \) \( 74695 q + 3 q^{3} - 98 q^{4} - 18 q^{5} - 69 q^{6} - 32 q^{7} + 67 q^{9} + 10 q^{10} + 100 q^{11} + 35 q^{12} - 150 q^{13} + 700 q^{14} + 166 q^{15} + 406 q^{16} - 662 q^{17} - 465 q^{18} - 1000 q^{19} - 1900 q^{20} - 766 q^{21} - 1360 q^{22} - 688 q^{23} - 657 q^{24} - 521 q^{25} - 100 q^{26} - 33 q^{27} + 1770 q^{28} + 1166 q^{29} + 1485 q^{30} + 2744 q^{31} + 105 q^{33} - 3610 q^{34} + 1016 q^{35} - 1061 q^{36} - 1086 q^{37} + 1300 q^{38} - 650 q^{39} + 4570 q^{40} - 4350 q^{41} + 4625 q^{42} - 4388 q^{43} + 3010 q^{44} - 3872 q^{45} + 4578 q^{46} - 928 q^{47} + 2005 q^{48} + 1513 q^{49} + 140 q^{50} + 804 q^{51} - 2910 q^{52} + 11054 q^{53} - 9963 q^{54} + 3940 q^{55} - 9040 q^{56} + 4060 q^{57} - 4790 q^{58} + 1356 q^{59} + 2645 q^{60} - 3846 q^{61} + 1252 q^{63} + 1318 q^{64} - 6540 q^{65} + 4175 q^{66} - 6348 q^{67} + 4130 q^{69} - 6470 q^{70} + 3320 q^{71} - 615 q^{72} + 406 q^{73} - 9500 q^{74} + 4767 q^{75} - 5110 q^{76} + 1820 q^{77} - 9305 q^{78} + 4712 q^{79} + 6820 q^{80} - 1213 q^{81} + 10190 q^{82} + 852 q^{83} + 5925 q^{84} + 10056 q^{85} + 13600 q^{86} - 702 q^{87} + 13820 q^{88} - 430 q^{89} + 10165 q^{90} - 3840 q^{91} + 30420 q^{92} + 6122 q^{93} + 27706 q^{94} + 4560 q^{95} + 12329 q^{96} + 1546 q^{97} - 3870 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1452))\)

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
1452.4.a \(\chi_{1452}(1, \cdot)\) 1452.4.a.a 1 1
1452.4.a.b 1
1452.4.a.c 1
1452.4.a.d 1
1452.4.a.e 1
1452.4.a.f 1
1452.4.a.g 1
1452.4.a.h 1
1452.4.a.i 1
1452.4.a.j 2
1452.4.a.k 2
1452.4.a.l 2
1452.4.a.m 2
1452.4.a.n 2
1452.4.a.o 4
1452.4.a.p 4
1452.4.a.q 4
1452.4.a.r 6
1452.4.a.s 6
1452.4.a.t 6
1452.4.a.u 6
1452.4.b \(\chi_{1452}(725, \cdot)\) n/a 108 1
1452.4.c \(\chi_{1452}(1211, \cdot)\) n/a 636 1
1452.4.h \(\chi_{1452}(967, \cdot)\) n/a 324 1
1452.4.i \(\chi_{1452}(493, \cdot)\) n/a 216 4
1452.4.j \(\chi_{1452}(403, \cdot)\) n/a 1296 4
1452.4.o \(\chi_{1452}(251, \cdot)\) n/a 2528 4
1452.4.p \(\chi_{1452}(161, \cdot)\) n/a 432 4
1452.4.q \(\chi_{1452}(133, \cdot)\) n/a 660 10
1452.4.r \(\chi_{1452}(43, \cdot)\) n/a 3960 10
1452.4.w \(\chi_{1452}(23, \cdot)\) n/a 7880 10
1452.4.x \(\chi_{1452}(65, \cdot)\) n/a 1320 10
1452.4.y \(\chi_{1452}(25, \cdot)\) n/a 2640 40
1452.4.z \(\chi_{1452}(17, \cdot)\) n/a 5280 40
1452.4.ba \(\chi_{1452}(47, \cdot)\) n/a 31520 40
1452.4.bf \(\chi_{1452}(7, \cdot)\) n/a 15840 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1452))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1452)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 1}\)