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Properties

Label 1850.2
Level 1850
Weight 2
Dimension 31473
Nonzero newspaces 36
Sturm bound 410400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(410400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1850))\).

Total New Old
Modular forms 104616 31473 73143
Cusp forms 100585 31473 69112
Eisenstein series 4031 0 4031

Trace form

\( 31473 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10}) \) \( 31473 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} - 16 q^{21} - 56 q^{22} - 32 q^{23} - 32 q^{24} - 70 q^{25} - 3 q^{26} + 8 q^{27} - 12 q^{28} + 16 q^{29} - 40 q^{30} + 92 q^{31} - 8 q^{32} + 88 q^{33} + 58 q^{34} + 40 q^{35} + 71 q^{36} + 117 q^{37} + 76 q^{38} + 116 q^{39} + 10 q^{40} + 152 q^{41} + 136 q^{42} + 80 q^{43} + 24 q^{44} - 30 q^{45} + 120 q^{46} + 52 q^{47} + 20 q^{48} + 72 q^{49} + 50 q^{50} + 24 q^{51} + 28 q^{52} + 18 q^{53} + 80 q^{54} + 40 q^{55} + 16 q^{56} + 60 q^{58} + 36 q^{59} + 49 q^{61} - 56 q^{62} + 36 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} + 12 q^{67} - 84 q^{68} + 56 q^{69} - 80 q^{70} + 56 q^{71} + 26 q^{72} + 60 q^{73} - 62 q^{74} - 120 q^{75} - 40 q^{76} - 56 q^{77} - 88 q^{78} + 72 q^{79} + 10 q^{80} + 226 q^{81} - 76 q^{82} - 116 q^{83} - 56 q^{84} - 30 q^{85} - 32 q^{86} + 68 q^{87} + 24 q^{88} + 15 q^{89} + 10 q^{90} + 112 q^{91} + 44 q^{92} + 244 q^{93} + 168 q^{94} + 120 q^{95} + 8 q^{96} + 300 q^{97} + 258 q^{98} + 372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)

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
1850.2.a \(\chi_{1850}(1, \cdot)\) 1850.2.a.a 1 1
1850.2.a.b 1
1850.2.a.c 1
1850.2.a.d 1
1850.2.a.e 1
1850.2.a.f 1
1850.2.a.g 1
1850.2.a.h 1
1850.2.a.i 1
1850.2.a.j 1
1850.2.a.k 1
1850.2.a.l 1
1850.2.a.m 1
1850.2.a.n 1
1850.2.a.o 1
1850.2.a.p 1
1850.2.a.q 2
1850.2.a.r 2
1850.2.a.s 2
1850.2.a.t 2
1850.2.a.u 2
1850.2.a.v 2
1850.2.a.w 2
1850.2.a.x 2
1850.2.a.y 3
1850.2.a.z 3
1850.2.a.ba 3
1850.2.a.bb 3
1850.2.a.bc 3
1850.2.a.bd 5
1850.2.a.be 5
1850.2.b \(\chi_{1850}(149, \cdot)\) 1850.2.b.a 2 1
1850.2.b.b 2
1850.2.b.c 2
1850.2.b.d 2
1850.2.b.e 2
1850.2.b.f 2
1850.2.b.g 2
1850.2.b.h 2
1850.2.b.i 4
1850.2.b.j 4
1850.2.b.k 4
1850.2.b.l 4
1850.2.b.m 4
1850.2.b.n 6
1850.2.b.o 6
1850.2.b.p 6
1850.2.c \(\chi_{1850}(1849, \cdot)\) 1850.2.c.a 2 1
1850.2.c.b 2
1850.2.c.c 2
1850.2.c.d 2
1850.2.c.e 2
1850.2.c.f 2
1850.2.c.g 4
1850.2.c.h 4
1850.2.c.i 6
1850.2.c.j 6
1850.2.c.k 12
1850.2.c.l 12
1850.2.d \(\chi_{1850}(1701, \cdot)\) 1850.2.d.a 2 1
1850.2.d.b 2
1850.2.d.c 2
1850.2.d.d 2
1850.2.d.e 4
1850.2.d.f 6
1850.2.d.g 12
1850.2.d.h 12
1850.2.d.i 20
1850.2.e \(\chi_{1850}(951, \cdot)\) n/a 122 2
1850.2.g \(\chi_{1850}(43, \cdot)\) n/a 114 2
1850.2.h \(\chi_{1850}(857, \cdot)\) n/a 114 2
1850.2.l \(\chi_{1850}(371, \cdot)\) n/a 360 4
1850.2.m \(\chi_{1850}(101, \cdot)\) n/a 124 2
1850.2.n \(\chi_{1850}(249, \cdot)\) n/a 112 2
1850.2.o \(\chi_{1850}(1099, \cdot)\) n/a 116 2
1850.2.p \(\chi_{1850}(201, \cdot)\) n/a 354 6
1850.2.q \(\chi_{1850}(221, \cdot)\) n/a 376 4
1850.2.r \(\chi_{1850}(369, \cdot)\) n/a 384 4
1850.2.s \(\chi_{1850}(519, \cdot)\) n/a 360 4
1850.2.u \(\chi_{1850}(643, \cdot)\) n/a 228 4
1850.2.v \(\chi_{1850}(193, \cdot)\) n/a 228 4
1850.2.z \(\chi_{1850}(121, \cdot)\) n/a 768 8
1850.2.ba \(\chi_{1850}(99, \cdot)\) n/a 336 6
1850.2.bb \(\chi_{1850}(151, \cdot)\) n/a 360 6
1850.2.bc \(\chi_{1850}(49, \cdot)\) n/a 348 6
1850.2.bg \(\chi_{1850}(117, \cdot)\) n/a 760 8
1850.2.bh \(\chi_{1850}(327, \cdot)\) n/a 760 8
1850.2.bj \(\chi_{1850}(269, \cdot)\) n/a 752 8
1850.2.bk \(\chi_{1850}(159, \cdot)\) n/a 768 8
1850.2.bl \(\chi_{1850}(11, \cdot)\) n/a 752 8
1850.2.bo \(\chi_{1850}(143, \cdot)\) n/a 684 12
1850.2.br \(\chi_{1850}(57, \cdot)\) n/a 684 12
1850.2.bs \(\chi_{1850}(71, \cdot)\) n/a 2304 24
1850.2.bw \(\chi_{1850}(23, \cdot)\) n/a 1520 16
1850.2.bx \(\chi_{1850}(97, \cdot)\) n/a 1520 16
1850.2.bz \(\chi_{1850}(9, \cdot)\) n/a 2256 24
1850.2.ca \(\chi_{1850}(21, \cdot)\) n/a 2256 24
1850.2.cb \(\chi_{1850}(139, \cdot)\) n/a 2304 24
1850.2.cc \(\chi_{1850}(13, \cdot)\) n/a 4560 48
1850.2.cf \(\chi_{1850}(17, \cdot)\) n/a 4560 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)\(^{\oplus 1}\)