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Properties

Label 2493.2
Level 2493
Weight 2
Dimension 180987
Nonzero newspaces 30
Sturm bound 920736
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(920736\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2493))\).

Total New Old
Modular forms 232392 183461 48931
Cusp forms 227977 180987 46990
Eisenstein series 4415 2474 1941

Trace form

\( 180987 q - 414 q^{2} - 552 q^{3} - 414 q^{4} - 414 q^{5} - 552 q^{6} - 414 q^{7} - 414 q^{8} - 552 q^{9} + O(q^{10}) \) \( 180987 q - 414 q^{2} - 552 q^{3} - 414 q^{4} - 414 q^{5} - 552 q^{6} - 414 q^{7} - 414 q^{8} - 552 q^{9} - 1242 q^{10} - 414 q^{11} - 552 q^{12} - 414 q^{13} - 414 q^{14} - 552 q^{15} - 414 q^{16} - 414 q^{17} - 552 q^{18} - 1242 q^{19} - 414 q^{20} - 552 q^{21} - 414 q^{22} - 414 q^{23} - 552 q^{24} - 414 q^{25} - 414 q^{26} - 552 q^{27} - 1242 q^{28} - 414 q^{29} - 552 q^{30} - 414 q^{31} - 414 q^{32} - 552 q^{33} - 414 q^{34} - 414 q^{35} - 552 q^{36} - 1242 q^{37} - 414 q^{38} - 552 q^{39} - 414 q^{40} - 414 q^{41} - 552 q^{42} - 414 q^{43} - 414 q^{44} - 552 q^{45} - 1242 q^{46} - 414 q^{47} - 552 q^{48} - 414 q^{49} - 414 q^{50} - 552 q^{51} - 414 q^{52} - 414 q^{53} - 552 q^{54} - 1242 q^{55} - 414 q^{56} - 552 q^{57} - 414 q^{58} - 414 q^{59} - 552 q^{60} - 414 q^{61} - 414 q^{62} - 552 q^{63} - 1242 q^{64} - 414 q^{65} - 552 q^{66} - 414 q^{67} - 414 q^{68} - 552 q^{69} - 414 q^{70} - 414 q^{71} - 552 q^{72} - 1242 q^{73} - 414 q^{74} - 552 q^{75} - 414 q^{76} - 414 q^{77} - 552 q^{78} - 414 q^{79} - 414 q^{80} - 552 q^{81} - 1242 q^{82} - 414 q^{83} - 552 q^{84} - 414 q^{85} - 414 q^{86} - 552 q^{87} - 414 q^{88} - 414 q^{89} - 552 q^{90} - 1242 q^{91} - 414 q^{92} - 552 q^{93} - 414 q^{94} - 414 q^{95} - 552 q^{96} - 414 q^{97} - 414 q^{98} - 552 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2493))\)

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
2493.2.a \(\chi_{2493}(1, \cdot)\) 2493.2.a.a 1 1
2493.2.a.b 1
2493.2.a.c 3
2493.2.a.d 3
2493.2.a.e 6
2493.2.a.f 9
2493.2.a.g 9
2493.2.a.h 17
2493.2.a.i 20
2493.2.a.j 20
2493.2.a.k 26
2493.2.c \(\chi_{2493}(2215, \cdot)\) n/a 116 1
2493.2.e \(\chi_{2493}(832, \cdot)\) n/a 552 2
2493.2.f \(\chi_{2493}(1501, \cdot)\) n/a 552 2
2493.2.g \(\chi_{2493}(160, \cdot)\) n/a 552 2
2493.2.h \(\chi_{2493}(991, \cdot)\) n/a 228 2
2493.2.i \(\chi_{2493}(494, \cdot)\) n/a 188 2
2493.2.k \(\chi_{2493}(1225, \cdot)\) n/a 230 2
2493.2.q \(\chi_{2493}(394, \cdot)\) n/a 552 2
2493.2.r \(\chi_{2493}(553, \cdot)\) n/a 552 2
2493.2.t \(\chi_{2493}(1546, \cdot)\) n/a 552 2
2493.2.x \(\chi_{2493}(35, \cdot)\) n/a 368 4
2493.2.z \(\chi_{2493}(95, \cdot)\) n/a 1104 4
2493.2.ba \(\chi_{2493}(182, \cdot)\) n/a 1104 4
2493.2.bd \(\chi_{2493}(614, \cdot)\) n/a 1104 4
2493.2.be \(\chi_{2493}(19, \cdot)\) n/a 2530 22
2493.2.bg \(\chi_{2493}(64, \cdot)\) n/a 2552 22
2493.2.bi \(\chi_{2493}(10, \cdot)\) n/a 5016 44
2493.2.bj \(\chi_{2493}(49, \cdot)\) n/a 12144 44
2493.2.bk \(\chi_{2493}(67, \cdot)\) n/a 12144 44
2493.2.bl \(\chi_{2493}(16, \cdot)\) n/a 12144 44
2493.2.bn \(\chi_{2493}(8, \cdot)\) n/a 4136 44
2493.2.bq \(\chi_{2493}(22, \cdot)\) n/a 12144 44
2493.2.bs \(\chi_{2493}(4, \cdot)\) n/a 12144 44
2493.2.bt \(\chi_{2493}(7, \cdot)\) n/a 12144 44
2493.2.bz \(\chi_{2493}(289, \cdot)\) n/a 5060 44
2493.2.ca \(\chi_{2493}(2, \cdot)\) n/a 24288 88
2493.2.cd \(\chi_{2493}(11, \cdot)\) n/a 24288 88
2493.2.ce \(\chi_{2493}(5, \cdot)\) n/a 24288 88
2493.2.cg \(\chi_{2493}(17, \cdot)\) n/a 8096 88

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2493))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2493)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(277))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(831))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2493))\)\(^{\oplus 1}\)