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Properties

Label 1098.2
Level 1098
Weight 2
Dimension 8831
Nonzero newspaces 30
Sturm bound 133920
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(133920\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1098))\).

Total New Old
Modular forms 34440 8831 25609
Cusp forms 32521 8831 23690
Eisenstein series 1919 0 1919

Trace form

\( 8831 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 8831 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} - 6 q^{36} + 16 q^{37} - 2 q^{38} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 24 q^{46} + 48 q^{47} - 6 q^{48} + 134 q^{49} + 65 q^{50} - 18 q^{51} + 79 q^{52} + 12 q^{53} - 18 q^{54} + 240 q^{55} + 64 q^{56} - 6 q^{57} + 132 q^{58} + 126 q^{59} + 268 q^{61} + 196 q^{62} + 24 q^{63} - 4 q^{64} + 120 q^{65} + 250 q^{67} + 54 q^{68} + 180 q^{70} + 108 q^{71} - 6 q^{72} + 76 q^{73} + 67 q^{74} + 30 q^{75} + 18 q^{76} + 48 q^{77} + 12 q^{78} - 8 q^{79} + 18 q^{81} - 36 q^{82} + 24 q^{83} + 12 q^{84} - 2 q^{86} - 36 q^{87} - 6 q^{88} - 24 q^{89} - 16 q^{91} - 12 q^{92} - 12 q^{94} + 10 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1098))\)

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
1098.2.a \(\chi_{1098}(1, \cdot)\) 1098.2.a.a 1 1
1098.2.a.b 1
1098.2.a.c 1
1098.2.a.d 1
1098.2.a.e 1
1098.2.a.f 1
1098.2.a.g 1
1098.2.a.h 1
1098.2.a.i 1
1098.2.a.j 1
1098.2.a.k 1
1098.2.a.l 1
1098.2.a.m 2
1098.2.a.n 2
1098.2.a.o 3
1098.2.a.p 3
1098.2.a.q 3
1098.2.d \(\chi_{1098}(487, \cdot)\) 1098.2.d.a 2 1
1098.2.d.b 4
1098.2.d.c 4
1098.2.d.d 6
1098.2.d.e 8
1098.2.e \(\chi_{1098}(367, \cdot)\) 1098.2.e.a 2 2
1098.2.e.b 2
1098.2.e.c 2
1098.2.e.d 22
1098.2.e.e 24
1098.2.e.f 34
1098.2.e.g 34
1098.2.f \(\chi_{1098}(379, \cdot)\) 1098.2.f.a 2 2
1098.2.f.b 2
1098.2.f.c 4
1098.2.f.d 4
1098.2.f.e 6
1098.2.f.f 6
1098.2.f.g 6
1098.2.f.h 12
1098.2.f.i 12
1098.2.g \(\chi_{1098}(13, \cdot)\) n/a 124 2
1098.2.h \(\chi_{1098}(535, \cdot)\) n/a 124 2
1098.2.j \(\chi_{1098}(233, \cdot)\) 1098.2.j.a 4 2
1098.2.j.b 16
1098.2.j.c 16
1098.2.k \(\chi_{1098}(217, \cdot)\) 1098.2.k.a 4 4
1098.2.k.b 4
1098.2.k.c 4
1098.2.k.d 4
1098.2.k.e 4
1098.2.k.f 8
1098.2.k.g 8
1098.2.k.h 12
1098.2.k.i 12
1098.2.k.j 12
1098.2.k.k 12
1098.2.k.l 16
1098.2.n \(\chi_{1098}(841, \cdot)\) n/a 124 2
1098.2.o \(\chi_{1098}(109, \cdot)\) 1098.2.o.a 8 2
1098.2.o.b 12
1098.2.o.c 12
1098.2.o.d 20
1098.2.p \(\chi_{1098}(121, \cdot)\) n/a 124 2
1098.2.w \(\chi_{1098}(319, \cdot)\) n/a 124 2
1098.2.x \(\chi_{1098}(163, \cdot)\) 1098.2.x.a 8 4
1098.2.x.b 8
1098.2.x.c 24
1098.2.x.d 24
1098.2.x.e 32
1098.2.bb \(\chi_{1098}(11, \cdot)\) n/a 248 4
1098.2.bc \(\chi_{1098}(29, \cdot)\) n/a 248 4
1098.2.bd \(\chi_{1098}(143, \cdot)\) 1098.2.bd.a 40 4
1098.2.bd.b 48
1098.2.bh \(\chi_{1098}(101, \cdot)\) n/a 248 4
1098.2.bi \(\chi_{1098}(103, \cdot)\) n/a 496 8
1098.2.bj \(\chi_{1098}(25, \cdot)\) n/a 496 8
1098.2.bk \(\chi_{1098}(241, \cdot)\) n/a 496 8
1098.2.bl \(\chi_{1098}(73, \cdot)\) n/a 216 8
1098.2.bm \(\chi_{1098}(53, \cdot)\) n/a 144 8
1098.2.bo \(\chi_{1098}(49, \cdot)\) n/a 496 8
1098.2.bv \(\chi_{1098}(19, \cdot)\) n/a 208 8
1098.2.bw \(\chi_{1098}(247, \cdot)\) n/a 496 8
1098.2.bx \(\chi_{1098}(97, \cdot)\) n/a 496 8
1098.2.ca \(\chi_{1098}(275, \cdot)\) n/a 992 16
1098.2.ce \(\chi_{1098}(17, \cdot)\) n/a 352 16
1098.2.cf \(\chi_{1098}(59, \cdot)\) n/a 992 16
1098.2.cg \(\chi_{1098}(23, \cdot)\) n/a 992 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1098))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1098)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(549))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1098))\)\(^{\oplus 1}\)