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Properties

Label 2416.2
Level 2416
Weight 2
Dimension 101921
Nonzero newspaces 24
Sturm bound 729600
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2416 = 2^{4} \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(729600\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2416))\).

Total New Old
Modular forms 184500 103261 81239
Cusp forms 180301 101921 78380
Eisenstein series 4199 1340 2859

Trace form

\( 101921 q - 296 q^{2} - 221 q^{3} - 300 q^{4} - 371 q^{5} - 308 q^{6} - 225 q^{7} - 308 q^{8} - 75 q^{9} + O(q^{10}) \) \( 101921 q - 296 q^{2} - 221 q^{3} - 300 q^{4} - 371 q^{5} - 308 q^{6} - 225 q^{7} - 308 q^{8} - 75 q^{9} - 300 q^{10} - 229 q^{11} - 292 q^{12} - 371 q^{13} - 292 q^{14} - 233 q^{15} - 284 q^{16} - 667 q^{17} - 304 q^{18} - 237 q^{19} - 308 q^{20} - 383 q^{21} - 300 q^{22} - 225 q^{23} - 300 q^{24} - 75 q^{25} - 308 q^{26} - 209 q^{27} - 316 q^{28} - 387 q^{29} - 292 q^{30} - 193 q^{31} - 316 q^{32} - 667 q^{33} - 308 q^{34} - 217 q^{35} - 292 q^{36} - 387 q^{37} - 276 q^{38} - 225 q^{39} - 284 q^{40} - 75 q^{41} - 300 q^{42} - 245 q^{43} - 292 q^{44} - 379 q^{45} - 324 q^{46} - 257 q^{47} - 316 q^{48} - 687 q^{49} - 288 q^{50} - 233 q^{51} - 292 q^{52} - 355 q^{53} - 300 q^{54} - 225 q^{55} - 284 q^{56} - 75 q^{57} - 276 q^{58} - 213 q^{59} - 300 q^{60} - 339 q^{61} - 332 q^{62} - 233 q^{63} - 300 q^{64} - 683 q^{65} - 308 q^{66} - 205 q^{67} - 300 q^{68} - 351 q^{69} - 316 q^{70} - 225 q^{71} - 308 q^{72} - 75 q^{73} - 300 q^{74} - 237 q^{75} - 324 q^{76} - 383 q^{77} - 292 q^{78} - 225 q^{79} - 316 q^{80} - 695 q^{81} - 300 q^{82} - 221 q^{83} - 284 q^{84} - 383 q^{85} - 300 q^{86} - 225 q^{87} - 316 q^{88} - 75 q^{89} - 292 q^{90} - 233 q^{91} - 252 q^{92} - 407 q^{93} - 268 q^{94} - 201 q^{95} - 268 q^{96} - 667 q^{97} - 288 q^{98} - 221 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2416))\)

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
2416.2.a \(\chi_{2416}(1, \cdot)\) 2416.2.a.a 1 1
2416.2.a.b 1
2416.2.a.c 1
2416.2.a.d 1
2416.2.a.e 2
2416.2.a.f 3
2416.2.a.g 3
2416.2.a.h 3
2416.2.a.i 3
2416.2.a.j 3
2416.2.a.k 4
2416.2.a.l 4
2416.2.a.m 4
2416.2.a.n 6
2416.2.a.o 6
2416.2.a.p 8
2416.2.a.q 11
2416.2.a.r 11
2416.2.b \(\chi_{2416}(1209, \cdot)\) None 0 1
2416.2.c \(\chi_{2416}(1207, \cdot)\) None 0 1
2416.2.h \(\chi_{2416}(2415, \cdot)\) 2416.2.h.a 24 1
2416.2.h.b 52
2416.2.i \(\chi_{2416}(1089, \cdot)\) n/a 150 2
2416.2.j \(\chi_{2416}(603, \cdot)\) n/a 604 2
2416.2.k \(\chi_{2416}(605, \cdot)\) n/a 600 2
2416.2.n \(\chi_{2416}(321, \cdot)\) n/a 300 4
2416.2.q \(\chi_{2416}(119, \cdot)\) None 0 2
2416.2.r \(\chi_{2416}(873, \cdot)\) None 0 2
2416.2.s \(\chi_{2416}(335, \cdot)\) n/a 152 2
2416.2.v \(\chi_{2416}(143, \cdot)\) n/a 304 4
2416.2.ba \(\chi_{2416}(87, \cdot)\) None 0 4
2416.2.bb \(\chi_{2416}(361, \cdot)\) None 0 4
2416.2.be \(\chi_{2416}(269, \cdot)\) n/a 1208 4
2416.2.bf \(\chi_{2416}(723, \cdot)\) n/a 1208 4
2416.2.bg \(\chi_{2416}(529, \cdot)\) n/a 600 8
2416.2.bj \(\chi_{2416}(461, \cdot)\) n/a 2416 8
2416.2.bk \(\chi_{2416}(243, \cdot)\) n/a 2416 8
2416.2.bl \(\chi_{2416}(81, \cdot)\) n/a 1500 20
2416.2.bo \(\chi_{2416}(415, \cdot)\) n/a 608 8
2416.2.bp \(\chi_{2416}(105, \cdot)\) None 0 8
2416.2.bq \(\chi_{2416}(23, \cdot)\) None 0 8
2416.2.bt \(\chi_{2416}(343, \cdot)\) None 0 20
2416.2.bw \(\chi_{2416}(79, \cdot)\) n/a 1520 20
2416.2.bx \(\chi_{2416}(9, \cdot)\) None 0 20
2416.2.ca \(\chi_{2416}(75, \cdot)\) n/a 4832 16
2416.2.cb \(\chi_{2416}(85, \cdot)\) n/a 4832 16
2416.2.ce \(\chi_{2416}(17, \cdot)\) n/a 3000 40
2416.2.ch \(\chi_{2416}(3, \cdot)\) n/a 12080 40
2416.2.ci \(\chi_{2416}(29, \cdot)\) n/a 12080 40
2416.2.cl \(\chi_{2416}(7, \cdot)\) None 0 40
2416.2.co \(\chi_{2416}(25, \cdot)\) None 0 40
2416.2.cp \(\chi_{2416}(15, \cdot)\) n/a 3040 40
2416.2.cq \(\chi_{2416}(5, \cdot)\) n/a 24160 80
2416.2.cr \(\chi_{2416}(35, \cdot)\) n/a 24160 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2416))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2416)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2416))\)\(^{\oplus 1}\)