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Properties

Label 1210.2
Level 1210
Weight 2
Dimension 13089
Nonzero newspaces 12
Sturm bound 174240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(174240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1210))\).

Total New Old
Modular forms 44840 13089 31751
Cusp forms 42281 13089 29192
Eisenstein series 2559 0 2559

Trace form

\( 13089 q - q^{2} - 4 q^{3} - q^{4} - q^{5} + 16 q^{6} + 32 q^{7} - q^{8} + 67 q^{9} + O(q^{10}) \) \( 13089 q - q^{2} - 4 q^{3} - q^{4} - q^{5} + 16 q^{6} + 32 q^{7} - q^{8} + 67 q^{9} + 19 q^{10} + 20 q^{11} + 36 q^{12} + 26 q^{13} + 32 q^{14} + 56 q^{15} - q^{16} + 62 q^{17} + 7 q^{18} + 40 q^{19} - q^{20} + 48 q^{21} + 56 q^{23} + 16 q^{24} + 79 q^{25} + 66 q^{26} + 140 q^{27} + 32 q^{28} + 130 q^{29} + 56 q^{30} + 88 q^{31} + 19 q^{32} + 110 q^{33} + 62 q^{34} + 112 q^{35} + 7 q^{36} + 42 q^{37} + 100 q^{38} + 144 q^{39} + 19 q^{40} + 118 q^{41} + 8 q^{42} - 4 q^{43} - 10 q^{44} - 153 q^{45} - 104 q^{46} - 128 q^{47} - 4 q^{48} - 217 q^{49} - 121 q^{50} - 132 q^{51} - 94 q^{52} - 94 q^{53} - 200 q^{54} - 90 q^{55} - 8 q^{56} - 60 q^{57} - 190 q^{58} - 40 q^{59} - 124 q^{60} - 102 q^{61} - 72 q^{62} - 24 q^{63} - q^{64} - 54 q^{65} + 40 q^{66} + 52 q^{67} - 18 q^{68} + 184 q^{69} - 8 q^{70} + 248 q^{71} + 67 q^{72} + 166 q^{73} + 42 q^{74} + 176 q^{75} + 20 q^{76} + 160 q^{77} + 104 q^{78} + 120 q^{79} + 19 q^{80} + 419 q^{81} + 98 q^{82} + 176 q^{83} + 128 q^{84} + 202 q^{85} + 216 q^{86} + 280 q^{87} + 20 q^{88} + 230 q^{89} + 167 q^{90} + 208 q^{91} + 96 q^{92} + 152 q^{93} + 192 q^{94} + 40 q^{95} - 4 q^{96} + 42 q^{97} + 123 q^{98} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)

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
1210.2.a \(\chi_{1210}(1, \cdot)\) 1210.2.a.a 1 1
1210.2.a.b 1
1210.2.a.c 1
1210.2.a.d 1
1210.2.a.e 1
1210.2.a.f 1
1210.2.a.g 1
1210.2.a.h 1
1210.2.a.i 1
1210.2.a.j 1
1210.2.a.k 1
1210.2.a.l 1
1210.2.a.m 1
1210.2.a.n 2
1210.2.a.o 2
1210.2.a.p 2
1210.2.a.q 2
1210.2.a.r 2
1210.2.a.s 2
1210.2.a.t 2
1210.2.a.u 4
1210.2.a.v 4
1210.2.b \(\chi_{1210}(969, \cdot)\) 1210.2.b.a 2 1
1210.2.b.b 2
1210.2.b.c 2
1210.2.b.d 2
1210.2.b.e 2
1210.2.b.f 4
1210.2.b.g 4
1210.2.b.h 4
1210.2.b.i 4
1210.2.b.j 4
1210.2.b.k 8
1210.2.b.l 8
1210.2.b.m 8
1210.2.f \(\chi_{1210}(483, \cdot)\) n/a 108 2
1210.2.g \(\chi_{1210}(81, \cdot)\) n/a 144 4
1210.2.j \(\chi_{1210}(9, \cdot)\) n/a 216 4
1210.2.k \(\chi_{1210}(111, \cdot)\) n/a 440 10
1210.2.l \(\chi_{1210}(233, \cdot)\) n/a 432 8
1210.2.o \(\chi_{1210}(89, \cdot)\) n/a 660 10
1210.2.q \(\chi_{1210}(43, \cdot)\) n/a 1320 20
1210.2.s \(\chi_{1210}(31, \cdot)\) n/a 1760 40
1210.2.u \(\chi_{1210}(49, \cdot)\) n/a 2640 40
1210.2.x \(\chi_{1210}(7, \cdot)\) n/a 5280 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1210))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1210)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)