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Properties

Label 2366.2
Level 2366
Weight 2
Dimension 53774
Nonzero newspaces 30
Sturm bound 681408
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(681408\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2366))\).

Total New Old
Modular forms 173088 53774 119314
Cusp forms 167617 53774 113843
Eisenstein series 5471 0 5471

Trace form

\( 53774 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{6} + 8 q^{7} + 10 q^{8} + 52 q^{9} + O(q^{10}) \) \( 53774 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{6} + 8 q^{7} + 10 q^{8} + 52 q^{9} + 54 q^{10} + 36 q^{11} + 10 q^{12} + 48 q^{13} + 22 q^{14} + 72 q^{15} + 16 q^{16} + 48 q^{17} + 46 q^{18} + 94 q^{19} + 6 q^{20} + 50 q^{21} - 12 q^{22} + 24 q^{23} - 2 q^{24} + 24 q^{25} + 108 q^{27} + 8 q^{28} + 120 q^{29} + 72 q^{30} + 124 q^{31} - 2 q^{32} + 192 q^{33} + 72 q^{34} + 138 q^{35} + 84 q^{36} + 88 q^{37} + 122 q^{38} + 104 q^{39} - 6 q^{40} + 168 q^{41} + 70 q^{42} + 140 q^{43} + 84 q^{44} + 222 q^{45} + 72 q^{46} + 132 q^{47} - 6 q^{48} + 64 q^{49} + 82 q^{50} + 204 q^{51} + 14 q^{52} + 96 q^{53} + 100 q^{54} + 168 q^{55} + 22 q^{56} + 172 q^{57} + 84 q^{58} + 126 q^{59} + 72 q^{60} + 102 q^{61} + 116 q^{62} + 236 q^{63} + 12 q^{64} + 174 q^{65} + 144 q^{66} + 232 q^{67} + 384 q^{69} + 66 q^{70} + 216 q^{71} + 82 q^{72} + 232 q^{73} - 28 q^{74} + 142 q^{75} - 98 q^{76} - 204 q^{77} - 24 q^{78} - 264 q^{79} + 6 q^{80} - 260 q^{81} - 420 q^{82} - 138 q^{83} - 286 q^{84} - 480 q^{85} - 244 q^{86} - 492 q^{87} - 12 q^{88} - 288 q^{89} - 558 q^{90} - 236 q^{91} - 216 q^{92} - 296 q^{93} - 516 q^{94} - 408 q^{95} - 2 q^{96} - 572 q^{97} - 194 q^{98} - 588 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2366))\)

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
2366.2.a \(\chi_{2366}(1, \cdot)\) 2366.2.a.a 1 1
2366.2.a.b 1
2366.2.a.c 1
2366.2.a.d 1
2366.2.a.e 1
2366.2.a.f 1
2366.2.a.g 1
2366.2.a.h 1
2366.2.a.i 1
2366.2.a.j 1
2366.2.a.k 1
2366.2.a.l 1
2366.2.a.m 1
2366.2.a.n 1
2366.2.a.o 1
2366.2.a.p 1
2366.2.a.q 2
2366.2.a.r 2
2366.2.a.s 2
2366.2.a.t 2
2366.2.a.u 3
2366.2.a.v 3
2366.2.a.w 3
2366.2.a.x 3
2366.2.a.y 3
2366.2.a.z 3
2366.2.a.ba 3
2366.2.a.bb 3
2366.2.a.bc 3
2366.2.a.bd 3
2366.2.a.be 6
2366.2.a.bf 6
2366.2.a.bg 6
2366.2.a.bh 6
2366.2.d \(\chi_{2366}(337, \cdot)\) 2366.2.d.a 2 1
2366.2.d.b 2
2366.2.d.c 2
2366.2.d.d 2
2366.2.d.e 2
2366.2.d.f 2
2366.2.d.g 2
2366.2.d.h 2
2366.2.d.i 2
2366.2.d.j 2
2366.2.d.k 4
2366.2.d.l 4
2366.2.d.m 6
2366.2.d.n 6
2366.2.d.o 6
2366.2.d.p 6
2366.2.d.q 12
2366.2.d.r 12
2366.2.e \(\chi_{2366}(529, \cdot)\) n/a 204 2
2366.2.f \(\chi_{2366}(1353, \cdot)\) n/a 208 2
2366.2.g \(\chi_{2366}(1205, \cdot)\) n/a 156 2
2366.2.h \(\chi_{2366}(191, \cdot)\) n/a 204 2
2366.2.i \(\chi_{2366}(2127, \cdot)\) n/a 200 2
2366.2.m \(\chi_{2366}(1037, \cdot)\) n/a 152 2
2366.2.n \(\chi_{2366}(1689, \cdot)\) n/a 208 2
2366.2.o \(\chi_{2366}(23, \cdot)\) n/a 204 2
2366.2.v \(\chi_{2366}(361, \cdot)\) n/a 204 2
2366.2.w \(\chi_{2366}(19, \cdot)\) n/a 408 4
2366.2.ba \(\chi_{2366}(587, \cdot)\) n/a 416 4
2366.2.bb \(\chi_{2366}(437, \cdot)\) n/a 416 4
2366.2.bc \(\chi_{2366}(89, \cdot)\) n/a 408 4
2366.2.be \(\chi_{2366}(183, \cdot)\) n/a 1080 12
2366.2.bf \(\chi_{2366}(155, \cdot)\) n/a 1104 12
2366.2.bi \(\chi_{2366}(9, \cdot)\) n/a 2928 24
2366.2.bj \(\chi_{2366}(29, \cdot)\) n/a 2160 24
2366.2.bk \(\chi_{2366}(53, \cdot)\) n/a 2880 24
2366.2.bl \(\chi_{2366}(107, \cdot)\) n/a 2928 24
2366.2.bn \(\chi_{2366}(83, \cdot)\) n/a 2976 24
2366.2.bo \(\chi_{2366}(121, \cdot)\) n/a 2928 24
2366.2.bv \(\chi_{2366}(95, \cdot)\) n/a 2928 24
2366.2.bw \(\chi_{2366}(25, \cdot)\) n/a 2880 24
2366.2.bx \(\chi_{2366}(43, \cdot)\) n/a 2208 24
2366.2.cb \(\chi_{2366}(45, \cdot)\) n/a 5856 48
2366.2.cc \(\chi_{2366}(5, \cdot)\) n/a 5760 48
2366.2.cd \(\chi_{2366}(41, \cdot)\) n/a 5760 48
2366.2.ch \(\chi_{2366}(33, \cdot)\) n/a 5856 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)