Properties

Label 95.11
Level 95
Weight 11
Dimension 3230
Nonzero newspaces 9
Newform subspaces 12
Sturm bound 7920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 12 \)
Sturm bound: \(7920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(95))\).

Total New Old
Modular forms 3672 3330 342
Cusp forms 3528 3230 298
Eisenstein series 144 100 44

Trace form

\( 3230 q - 78 q^{2} - 138 q^{3} - 18 q^{4} + 10653 q^{5} - 34086 q^{6} + 28982 q^{7} - 44058 q^{8} - 18 q^{9} + O(q^{10}) \) \( 3230 q - 78 q^{2} - 138 q^{3} - 18 q^{4} + 10653 q^{5} - 34086 q^{6} + 28982 q^{7} - 44058 q^{8} - 18 q^{9} + 322553 q^{10} + 467514 q^{11} + 1259646 q^{12} - 4233658 q^{13} + 3674862 q^{14} + 9215859 q^{15} - 8855590 q^{16} - 7945920 q^{17} - 25608456 q^{18} + 21917892 q^{19} + 53957538 q^{20} + 33952044 q^{21} - 114401234 q^{22} - 69774228 q^{23} + 44789742 q^{24} + 119747399 q^{25} + 122357154 q^{26} - 238181454 q^{27} + 326776 q^{28} - 177911730 q^{29} + 11977752 q^{30} + 122259490 q^{31} + 613050972 q^{32} + 293503470 q^{33} - 373029048 q^{34} - 548906139 q^{35} - 1480729122 q^{36} - 184432276 q^{37} + 1614989388 q^{38} + 1579614228 q^{39} - 151719702 q^{40} - 254735670 q^{41} - 1654851198 q^{42} - 2276310028 q^{43} + 1254448260 q^{44} - 750958722 q^{45} - 1963942196 q^{46} + 1169124468 q^{47} + 3874106616 q^{48} - 464842236 q^{49} - 949666068 q^{50} + 7497085992 q^{51} - 2214130090 q^{52} - 1056153642 q^{53} - 6669100404 q^{54} - 1534788263 q^{55} - 1705831272 q^{56} + 2055683412 q^{57} + 683141820 q^{58} + 7884604512 q^{59} + 9980591736 q^{60} + 19858467754 q^{61} - 1450015836 q^{62} - 28905467490 q^{63} - 43341908034 q^{64} - 2828618412 q^{65} + 18722460858 q^{66} + 23591314568 q^{67} + 40982277972 q^{68} + 22209160320 q^{69} + 7991322537 q^{70} - 27374389728 q^{71} - 72207962244 q^{72} - 22712550076 q^{73} - 20439782370 q^{74} - 10758005436 q^{75} + 34045267566 q^{76} + 48985793970 q^{77} - 1480985814 q^{78} + 32229277842 q^{79} + 48534178125 q^{80} + 27483453918 q^{81} - 17075410184 q^{82} - 6271933980 q^{83} - 161009954298 q^{84} - 108382268695 q^{85} - 106565068212 q^{86} + 7248491838 q^{87} + 124526509950 q^{88} + 98086756392 q^{89} + 149343966288 q^{90} + 15959730178 q^{91} + 4801419480 q^{92} + 70664719206 q^{93} + 7038605574 q^{95} - 69580003260 q^{96} - 90984729568 q^{97} - 351655980144 q^{98} - 249739320438 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(95))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
95.11.c \(\chi_{95}(56, \cdot)\) 95.11.c.a 68 1
95.11.d \(\chi_{95}(94, \cdot)\) 95.11.d.a 2 1
95.11.d.b 4
95.11.d.c 4
95.11.d.d 88
95.11.f \(\chi_{95}(58, \cdot)\) 95.11.f.a 180 2
95.11.h \(\chi_{95}(69, \cdot)\) 95.11.h.a 196 2
95.11.j \(\chi_{95}(31, \cdot)\) 95.11.j.a 136 2
95.11.m \(\chi_{95}(7, \cdot)\) 95.11.m.a 392 4
95.11.n \(\chi_{95}(21, \cdot)\) 95.11.n.a 396 6
95.11.o \(\chi_{95}(14, \cdot)\) 95.11.o.a 588 6
95.11.q \(\chi_{95}(17, \cdot)\) 95.11.q.a 1176 12

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)