Properties

Label 1350.2
Level 1350
Weight 2
Dimension 11798
Nonzero newspaces 18
Sturm bound 194400
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(194400\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1350))\).

Total New Old
Modular forms 50280 11798 38482
Cusp forms 46921 11798 35123
Eisenstein series 3359 0 3359

Trace form

\(11798q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11798q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut -\mathstrut 50q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 42q^{13} \) \(\mathstrut -\mathstrut 36q^{14} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 54q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 30q^{23} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut +\mathstrut 32q^{26} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 75q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut +\mathstrut 60q^{37} \) \(\mathstrut +\mathstrut 227q^{38} \) \(\mathstrut +\mathstrut 198q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut +\mathstrut 298q^{41} \) \(\mathstrut +\mathstrut 168q^{42} \) \(\mathstrut +\mathstrut 228q^{43} \) \(\mathstrut +\mathstrut 80q^{44} \) \(\mathstrut +\mathstrut 120q^{45} \) \(\mathstrut +\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 378q^{47} \) \(\mathstrut +\mathstrut 42q^{48} \) \(\mathstrut +\mathstrut 213q^{49} \) \(\mathstrut +\mathstrut 160q^{50} \) \(\mathstrut +\mathstrut 192q^{51} \) \(\mathstrut +\mathstrut 54q^{52} \) \(\mathstrut +\mathstrut 336q^{53} \) \(\mathstrut +\mathstrut 108q^{54} \) \(\mathstrut +\mathstrut 32q^{55} \) \(\mathstrut +\mathstrut 76q^{56} \) \(\mathstrut +\mathstrut 135q^{57} \) \(\mathstrut +\mathstrut 46q^{58} \) \(\mathstrut +\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 56q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 5q^{64} \) \(\mathstrut +\mathstrut 144q^{65} \) \(\mathstrut +\mathstrut 114q^{67} \) \(\mathstrut +\mathstrut 57q^{68} \) \(\mathstrut +\mathstrut 18q^{69} \) \(\mathstrut +\mathstrut 128q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 134q^{73} \) \(\mathstrut +\mathstrut 146q^{74} \) \(\mathstrut +\mathstrut 72q^{75} \) \(\mathstrut +\mathstrut 39q^{76} \) \(\mathstrut +\mathstrut 548q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut +\mathstrut 364q^{79} \) \(\mathstrut +\mathstrut 192q^{81} \) \(\mathstrut +\mathstrut 126q^{82} \) \(\mathstrut +\mathstrut 580q^{83} \) \(\mathstrut +\mathstrut 208q^{85} \) \(\mathstrut +\mathstrut 34q^{86} \) \(\mathstrut +\mathstrut 276q^{87} \) \(\mathstrut +\mathstrut 11q^{88} \) \(\mathstrut +\mathstrut 505q^{89} \) \(\mathstrut +\mathstrut 206q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 282q^{93} \) \(\mathstrut -\mathstrut 34q^{94} \) \(\mathstrut +\mathstrut 136q^{95} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 84q^{97} \) \(\mathstrut -\mathstrut 105q^{98} \) \(\mathstrut +\mathstrut 204q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)

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
1350.2.a \(\chi_{1350}(1, \cdot)\) 1350.2.a.a 1 1
1350.2.a.b 1
1350.2.a.c 1
1350.2.a.d 1
1350.2.a.e 1
1350.2.a.f 1
1350.2.a.g 1
1350.2.a.h 1
1350.2.a.i 1
1350.2.a.j 1
1350.2.a.k 1
1350.2.a.l 1
1350.2.a.m 1
1350.2.a.n 1
1350.2.a.o 1
1350.2.a.p 1
1350.2.a.q 1
1350.2.a.r 1
1350.2.a.s 1
1350.2.a.t 1
1350.2.a.u 1
1350.2.a.v 1
1350.2.a.w 2
1350.2.a.x 2
1350.2.c \(\chi_{1350}(649, \cdot)\) 1350.2.c.a 2 1
1350.2.c.b 2
1350.2.c.c 2
1350.2.c.d 2
1350.2.c.e 2
1350.2.c.f 2
1350.2.c.g 2
1350.2.c.h 2
1350.2.c.i 2
1350.2.c.j 2
1350.2.c.k 2
1350.2.c.l 2
1350.2.e \(\chi_{1350}(451, \cdot)\) 1350.2.e.a 2 2
1350.2.e.b 2
1350.2.e.c 2
1350.2.e.d 2
1350.2.e.e 2
1350.2.e.f 2
1350.2.e.g 2
1350.2.e.h 2
1350.2.e.i 2
1350.2.e.j 4
1350.2.e.k 4
1350.2.e.l 4
1350.2.e.m 4
1350.2.e.n 4
1350.2.f \(\chi_{1350}(107, \cdot)\) 1350.2.f.a 8 2
1350.2.f.b 8
1350.2.f.c 8
1350.2.f.d 8
1350.2.f.e 8
1350.2.f.f 8
1350.2.h \(\chi_{1350}(271, \cdot)\) n/a 160 4
1350.2.j \(\chi_{1350}(199, \cdot)\) 1350.2.j.a 4 2
1350.2.j.b 4
1350.2.j.c 4
1350.2.j.d 4
1350.2.j.e 4
1350.2.j.f 8
1350.2.j.g 8
1350.2.l \(\chi_{1350}(151, \cdot)\) n/a 342 6
1350.2.m \(\chi_{1350}(109, \cdot)\) n/a 160 4
1350.2.q \(\chi_{1350}(143, \cdot)\) 1350.2.q.a 8 4
1350.2.q.b 8
1350.2.q.c 8
1350.2.q.d 8
1350.2.q.e 8
1350.2.q.f 8
1350.2.q.g 8
1350.2.q.h 16
1350.2.r \(\chi_{1350}(91, \cdot)\) n/a 240 8
1350.2.u \(\chi_{1350}(49, \cdot)\) n/a 324 6
1350.2.w \(\chi_{1350}(53, \cdot)\) n/a 320 8
1350.2.z \(\chi_{1350}(19, \cdot)\) n/a 240 8
1350.2.bb \(\chi_{1350}(257, \cdot)\) n/a 648 12
1350.2.bc \(\chi_{1350}(31, \cdot)\) n/a 2160 24
1350.2.bd \(\chi_{1350}(17, \cdot)\) n/a 480 16
1350.2.bf \(\chi_{1350}(79, \cdot)\) n/a 2160 24
1350.2.bi \(\chi_{1350}(23, \cdot)\) n/a 4320 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1350)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)