Properties

Label 1323.2
Level 1323
Weight 2
Dimension 47373
Nonzero newspaces 32
Sturm bound 254016
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(254016\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1323))\).

Total New Old
Modular forms 65304 48925 16379
Cusp forms 61705 47373 14332
Eisenstein series 3599 1552 2047

Trace form

\( 47373q - 126q^{2} - 186q^{3} - 218q^{4} - 123q^{5} - 180q^{6} - 252q^{7} - 210q^{8} - 180q^{9} + O(q^{10}) \) \( 47373q - 126q^{2} - 186q^{3} - 218q^{4} - 123q^{5} - 180q^{6} - 252q^{7} - 210q^{8} - 180q^{9} - 213q^{10} - 117q^{11} - 168q^{12} - 207q^{13} - 132q^{14} - 315q^{15} - 166q^{16} - 75q^{17} - 171q^{18} - 192q^{19} - 39q^{20} - 216q^{21} - 327q^{22} - 96q^{23} - 198q^{24} - 184q^{25} - 78q^{26} - 189q^{27} - 556q^{28} - 198q^{29} - 189q^{30} - 183q^{31} - 12q^{32} - 180q^{33} - 129q^{34} - 108q^{35} - 306q^{36} - 154q^{37} + 42q^{38} - 147q^{39} - 117q^{40} + 3q^{41} - 216q^{42} - 319q^{43} + 39q^{44} - 189q^{45} - 93q^{46} - 63q^{47} - 411q^{48} - 250q^{49} - 537q^{50} - 306q^{51} - 315q^{52} - 390q^{53} - 450q^{54} - 660q^{55} - 402q^{56} - 471q^{57} - 453q^{58} - 432q^{59} - 612q^{60} - 315q^{61} - 672q^{62} - 342q^{63} - 758q^{64} - 477q^{65} - 477q^{66} - 320q^{67} - 747q^{68} - 351q^{69} - 336q^{70} - 333q^{71} - 522q^{72} - 315q^{73} - 279q^{74} - 321q^{75} - 276q^{76} - 162q^{77} - 450q^{78} - 167q^{79} - 282q^{80} - 144q^{81} - 396q^{82} + 75q^{83} - 216q^{84} - 261q^{85} + 195q^{86} - 171q^{87} - 120q^{88} + 117q^{89} - 162q^{90} - 172q^{91} + 57q^{92} - 219q^{93} + 15q^{94} + 87q^{95} - 180q^{96} - 66q^{97} - 6q^{98} - 603q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)

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
1323.2.a \(\chi_{1323}(1, \cdot)\) 1323.2.a.a 1 1
1323.2.a.b 1
1323.2.a.c 1
1323.2.a.d 1
1323.2.a.e 1
1323.2.a.f 1
1323.2.a.g 1
1323.2.a.h 1
1323.2.a.i 1
1323.2.a.j 1
1323.2.a.k 1
1323.2.a.l 1
1323.2.a.m 1
1323.2.a.n 1
1323.2.a.o 1
1323.2.a.p 1
1323.2.a.q 1
1323.2.a.r 1
1323.2.a.s 1
1323.2.a.t 2
1323.2.a.u 2
1323.2.a.v 2
1323.2.a.w 2
1323.2.a.x 3
1323.2.a.y 3
1323.2.a.z 3
1323.2.a.ba 3
1323.2.a.bb 4
1323.2.a.bc 4
1323.2.a.bd 4
1323.2.a.be 4
1323.2.c \(\chi_{1323}(1322, \cdot)\) 1323.2.c.a 2 1
1323.2.c.b 4
1323.2.c.c 4
1323.2.c.d 12
1323.2.c.e 16
1323.2.c.f 16
1323.2.e \(\chi_{1323}(1108, \cdot)\) n/a 106 2
1323.2.f \(\chi_{1323}(442, \cdot)\) 1323.2.f.a 2 2
1323.2.f.b 2
1323.2.f.c 6
1323.2.f.d 6
1323.2.f.e 10
1323.2.f.f 10
1323.2.f.g 12
1323.2.f.h 24
1323.2.g \(\chi_{1323}(361, \cdot)\) 1323.2.g.a 2 2
1323.2.g.b 6
1323.2.g.c 6
1323.2.g.d 6
1323.2.g.e 6
1323.2.g.f 10
1323.2.g.g 12
1323.2.g.h 24
1323.2.h \(\chi_{1323}(226, \cdot)\) 1323.2.h.a 2 2
1323.2.h.b 6
1323.2.h.c 6
1323.2.h.d 6
1323.2.h.e 6
1323.2.h.f 10
1323.2.h.g 12
1323.2.h.h 24
1323.2.i \(\chi_{1323}(521, \cdot)\) 1323.2.i.a 2 2
1323.2.i.b 10
1323.2.i.c 12
1323.2.i.d 48
1323.2.o \(\chi_{1323}(440, \cdot)\) 1323.2.o.a 2 2
1323.2.o.b 2
1323.2.o.c 10
1323.2.o.d 10
1323.2.o.e 48
1323.2.p \(\chi_{1323}(80, \cdot)\) n/a 106 2
1323.2.s \(\chi_{1323}(656, \cdot)\) 1323.2.s.a 2 2
1323.2.s.b 10
1323.2.s.c 12
1323.2.s.d 48
1323.2.u \(\chi_{1323}(190, \cdot)\) n/a 444 6
1323.2.v \(\chi_{1323}(67, \cdot)\) n/a 696 6
1323.2.w \(\chi_{1323}(148, \cdot)\) n/a 708 6
1323.2.x \(\chi_{1323}(214, \cdot)\) n/a 696 6
1323.2.z \(\chi_{1323}(188, \cdot)\) n/a 444 6
1323.2.be \(\chi_{1323}(68, \cdot)\) n/a 696 6
1323.2.bh \(\chi_{1323}(362, \cdot)\) n/a 696 6
1323.2.bi \(\chi_{1323}(146, \cdot)\) n/a 696 6
1323.2.bk \(\chi_{1323}(37, \cdot)\) n/a 648 12
1323.2.bl \(\chi_{1323}(100, \cdot)\) n/a 648 12
1323.2.bm \(\chi_{1323}(64, \cdot)\) n/a 648 12
1323.2.bn \(\chi_{1323}(109, \cdot)\) n/a 900 12
1323.2.bp \(\chi_{1323}(17, \cdot)\) n/a 648 12
1323.2.bs \(\chi_{1323}(26, \cdot)\) n/a 900 12
1323.2.bt \(\chi_{1323}(62, \cdot)\) n/a 648 12
1323.2.bz \(\chi_{1323}(143, \cdot)\) n/a 648 12
1323.2.ca \(\chi_{1323}(25, \cdot)\) n/a 5976 36
1323.2.cb \(\chi_{1323}(22, \cdot)\) n/a 5976 36
1323.2.cc \(\chi_{1323}(4, \cdot)\) n/a 5976 36
1323.2.ce \(\chi_{1323}(20, \cdot)\) n/a 5976 36
1323.2.cf \(\chi_{1323}(47, \cdot)\) n/a 5976 36
1323.2.ci \(\chi_{1323}(5, \cdot)\) n/a 5976 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1323))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1323)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)