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Properties

Label 2150.2
Level 2150
Weight 2
Dimension 42533
Nonzero newspaces 24
Sturm bound 554400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2150 = 2 \cdot 5^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(554400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2150))\).

Total New Old
Modular forms 140952 42533 98419
Cusp forms 136249 42533 93716
Eisenstein series 4703 0 4703

Trace form

\( 42533 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10}) \) \( 42533 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} - 16 q^{21} - 56 q^{22} - 32 q^{23} - 32 q^{24} - 70 q^{25} - 12 q^{26} - 40 q^{27} - 24 q^{28} - 20 q^{29} - 40 q^{30} - 2 q^{31} - 8 q^{32} + 100 q^{33} + 49 q^{34} + 40 q^{35} + 82 q^{36} + 150 q^{37} + 124 q^{38} + 130 q^{39} + 10 q^{40} + 86 q^{41} + 148 q^{42} + 214 q^{43} + 66 q^{44} - 30 q^{45} + 132 q^{46} + 58 q^{47} + 8 q^{48} + 122 q^{49} + 50 q^{50} + 108 q^{51} + 84 q^{52} + 102 q^{53} + 143 q^{54} + 40 q^{55} + 16 q^{56} + 14 q^{57} + 60 q^{58} + 4 q^{61} - 56 q^{62} - 72 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} - 24 q^{67} - 84 q^{68} - 46 q^{69} - 80 q^{70} + 26 q^{71} + 26 q^{72} + 30 q^{73} - 124 q^{74} - 120 q^{75} - 40 q^{76} - 2 q^{77} - 88 q^{78} + 84 q^{79} + 10 q^{80} + 250 q^{81} - 76 q^{82} - 68 q^{83} - 56 q^{84} - 30 q^{85} - 16 q^{86} + 170 q^{87} + 24 q^{88} + 54 q^{89} + 10 q^{90} + 148 q^{91} + 8 q^{92} + 304 q^{93} + 96 q^{94} + 120 q^{95} + 8 q^{96} + 282 q^{97} + 114 q^{98} + 339 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2150))\)

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
2150.2.a \(\chi_{2150}(1, \cdot)\) 2150.2.a.a 1 1
2150.2.a.b 1
2150.2.a.c 1
2150.2.a.d 1
2150.2.a.e 1
2150.2.a.f 1
2150.2.a.g 1
2150.2.a.h 1
2150.2.a.i 1
2150.2.a.j 1
2150.2.a.k 1
2150.2.a.l 1
2150.2.a.m 1
2150.2.a.n 1
2150.2.a.o 1
2150.2.a.p 1
2150.2.a.q 1
2150.2.a.r 1
2150.2.a.s 2
2150.2.a.t 2
2150.2.a.u 2
2150.2.a.v 2
2150.2.a.w 2
2150.2.a.x 2
2150.2.a.y 2
2150.2.a.z 2
2150.2.a.ba 2
2150.2.a.bb 3
2150.2.a.bc 3
2150.2.a.bd 3
2150.2.a.be 3
2150.2.a.bf 3
2150.2.a.bg 8
2150.2.a.bh 8
2150.2.b \(\chi_{2150}(1549, \cdot)\) 2150.2.b.a 2 1
2150.2.b.b 2
2150.2.b.c 2
2150.2.b.d 2
2150.2.b.e 2
2150.2.b.f 2
2150.2.b.g 2
2150.2.b.h 2
2150.2.b.i 2
2150.2.b.j 2
2150.2.b.k 2
2150.2.b.l 4
2150.2.b.m 4
2150.2.b.n 4
2150.2.b.o 4
2150.2.b.p 4
2150.2.b.q 4
2150.2.b.r 4
2150.2.b.s 6
2150.2.b.t 6
2150.2.e \(\chi_{2150}(251, \cdot)\) n/a 138 2
2150.2.g \(\chi_{2150}(257, \cdot)\) n/a 132 2
2150.2.h \(\chi_{2150}(431, \cdot)\) n/a 416 4
2150.2.k \(\chi_{2150}(49, \cdot)\) n/a 132 2
2150.2.l \(\chi_{2150}(451, \cdot)\) n/a 426 6
2150.2.o \(\chi_{2150}(259, \cdot)\) n/a 424 4
2150.2.p \(\chi_{2150}(7, \cdot)\) n/a 264 4
2150.2.t \(\chi_{2150}(299, \cdot)\) n/a 396 6
2150.2.u \(\chi_{2150}(221, \cdot)\) n/a 880 8
2150.2.v \(\chi_{2150}(687, \cdot)\) n/a 880 8
2150.2.x \(\chi_{2150}(101, \cdot)\) n/a 828 12
2150.2.y \(\chi_{2150}(457, \cdot)\) n/a 792 12
2150.2.ba \(\chi_{2150}(79, \cdot)\) n/a 880 8
2150.2.bd \(\chi_{2150}(11, \cdot)\) n/a 2640 24
2150.2.be \(\chi_{2150}(99, \cdot)\) n/a 792 12
2150.2.bi \(\chi_{2150}(37, \cdot)\) n/a 1760 16
2150.2.bj \(\chi_{2150}(59, \cdot)\) n/a 2640 24
2150.2.bn \(\chi_{2150}(157, \cdot)\) n/a 1584 24
2150.2.bo \(\chi_{2150}(31, \cdot)\) n/a 5280 48
2150.2.bq \(\chi_{2150}(27, \cdot)\) n/a 5280 48
2150.2.bt \(\chi_{2150}(9, \cdot)\) n/a 5280 48
2150.2.bu \(\chi_{2150}(3, \cdot)\) n/a 10560 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1075))\)\(^{\oplus 2}\)