Properties

Label 1452.2
Level 1452
Weight 2
Dimension 24710
Nonzero newspaces 16
Sturm bound 232320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(232320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1452))\).

Total New Old
Modular forms 59680 25274 34406
Cusp forms 56481 24710 31771
Eisenstein series 3199 564 2635

Trace form

\( 24710 q - 90 q^{4} - 45 q^{6} - 20 q^{7} - 110 q^{9} + O(q^{10}) \) \( 24710 q - 90 q^{4} - 45 q^{6} - 20 q^{7} - 110 q^{9} - 70 q^{10} - 10 q^{11} - 85 q^{12} - 200 q^{13} + 20 q^{14} - 10 q^{16} + 20 q^{17} - 25 q^{18} + 60 q^{19} + 100 q^{20} - 30 q^{21} - 40 q^{22} + 40 q^{23} + 15 q^{24} - 100 q^{25} + 100 q^{26} + 30 q^{27} + 10 q^{28} + 40 q^{29} - 35 q^{30} + 40 q^{31} - 60 q^{33} - 250 q^{34} + 40 q^{35} - 125 q^{36} - 20 q^{37} - 100 q^{38} + 70 q^{39} - 230 q^{40} + 120 q^{41} - 175 q^{42} - 70 q^{44} - 20 q^{45} - 190 q^{46} - 20 q^{47} - 155 q^{48} - 160 q^{49} - 140 q^{50} - 10 q^{51} - 190 q^{52} + 100 q^{53} - 195 q^{54} - 20 q^{55} - 80 q^{56} - 180 q^{57} - 110 q^{58} - 60 q^{59} - 235 q^{60} - 280 q^{61} - 130 q^{63} - 90 q^{64} - 120 q^{65} - 115 q^{66} - 100 q^{67} - 180 q^{69} - 230 q^{70} - 80 q^{71} - 215 q^{72} - 280 q^{73} - 100 q^{74} - 150 q^{75} - 230 q^{76} - 50 q^{77} - 305 q^{78} - 60 q^{79} - 220 q^{80} - 190 q^{81} - 290 q^{82} - 60 q^{83} - 195 q^{84} - 280 q^{85} - 160 q^{86} - 260 q^{88} - 80 q^{89} - 15 q^{90} + 100 q^{91} - 60 q^{92} - 50 q^{93} - 190 q^{94} + 60 q^{95} + 25 q^{96} - 60 q^{97} + 90 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1452))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1452.2.a \(\chi_{1452}(1, \cdot)\) 1452.2.a.a 1 1
1452.2.a.b 1
1452.2.a.c 1
1452.2.a.d 1
1452.2.a.e 1
1452.2.a.f 1
1452.2.a.g 1
1452.2.a.h 1
1452.2.a.i 2
1452.2.a.j 2
1452.2.a.k 2
1452.2.a.l 2
1452.2.a.m 2
1452.2.b \(\chi_{1452}(725, \cdot)\) 1452.2.b.a 4 1
1452.2.b.b 4
1452.2.b.c 4
1452.2.b.d 8
1452.2.b.e 16
1452.2.c \(\chi_{1452}(1211, \cdot)\) n/a 200 1
1452.2.h \(\chi_{1452}(967, \cdot)\) n/a 108 1
1452.2.i \(\chi_{1452}(493, \cdot)\) 1452.2.i.a 4 4
1452.2.i.b 4
1452.2.i.c 4
1452.2.i.d 4
1452.2.i.e 4
1452.2.i.f 4
1452.2.i.g 4
1452.2.i.h 4
1452.2.i.i 4
1452.2.i.j 4
1452.2.i.k 4
1452.2.i.l 4
1452.2.i.m 4
1452.2.i.n 4
1452.2.i.o 4
1452.2.i.p 4
1452.2.i.q 8
1452.2.j \(\chi_{1452}(403, \cdot)\) n/a 432 4
1452.2.o \(\chi_{1452}(251, \cdot)\) n/a 800 4
1452.2.p \(\chi_{1452}(161, \cdot)\) n/a 144 4
1452.2.q \(\chi_{1452}(133, \cdot)\) n/a 220 10
1452.2.r \(\chi_{1452}(43, \cdot)\) n/a 1320 10
1452.2.w \(\chi_{1452}(23, \cdot)\) n/a 2600 10
1452.2.x \(\chi_{1452}(65, \cdot)\) n/a 440 10
1452.2.y \(\chi_{1452}(25, \cdot)\) n/a 880 40
1452.2.z \(\chi_{1452}(17, \cdot)\) n/a 1760 40
1452.2.ba \(\chi_{1452}(47, \cdot)\) n/a 10400 40
1452.2.bf \(\chi_{1452}(7, \cdot)\) n/a 5280 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1452))\) into lower level spaces

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