Properties

Label 1205.2
Level 1205
Weight 2
Dimension 52519
Nonzero newspaces 40
Sturm bound 232320
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1205 = 5 \cdot 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(232320\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1205))\).

Total New Old
Modular forms 59040 53955 5085
Cusp forms 57121 52519 4602
Eisenstein series 1919 1436 483

Trace form

\( 52519q - 243q^{2} - 244q^{3} - 247q^{4} - 361q^{5} - 732q^{6} - 248q^{7} - 255q^{8} - 253q^{9} + O(q^{10}) \) \( 52519q - 243q^{2} - 244q^{3} - 247q^{4} - 361q^{5} - 732q^{6} - 248q^{7} - 255q^{8} - 253q^{9} - 363q^{10} - 732q^{11} - 268q^{12} - 254q^{13} - 264q^{14} - 364q^{15} - 751q^{16} - 258q^{17} - 279q^{18} - 260q^{19} - 367q^{20} - 752q^{21} - 276q^{22} - 264q^{23} - 300q^{24} - 361q^{25} - 762q^{26} - 280q^{27} - 296q^{28} - 270q^{29} - 372q^{30} - 752q^{31} - 303q^{32} - 288q^{33} - 294q^{34} - 368q^{35} - 811q^{36} - 278q^{37} - 300q^{38} - 296q^{39} - 375q^{40} - 762q^{41} - 336q^{42} - 284q^{43} - 324q^{44} - 373q^{45} - 792q^{46} - 288q^{47} - 364q^{48} - 297q^{49} - 363q^{50} - 792q^{51} - 338q^{52} - 294q^{53} - 360q^{54} - 372q^{55} - 840q^{56} - 320q^{57} - 330q^{58} - 300q^{59} - 388q^{60} - 782q^{61} - 336q^{62} - 344q^{63} - 367q^{64} - 374q^{65} - 864q^{66} - 308q^{67} - 366q^{68} - 336q^{69} - 384q^{70} - 792q^{71} - 435q^{72} - 314q^{73} - 354q^{74} - 364q^{75} - 860q^{76} - 336q^{77} - 408q^{78} - 320q^{79} - 391q^{80} - 841q^{81} - 366q^{82} - 324q^{83} - 464q^{84} - 378q^{85} - 852q^{86} - 360q^{87} - 420q^{88} - 330q^{89} - 399q^{90} - 832q^{91} - 408q^{92} - 368q^{93} - 384q^{94} - 380q^{95} - 972q^{96} - 338q^{97} - 411q^{98} - 396q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1205))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1205.2.a \(\chi_{1205}(1, \cdot)\) 1205.2.a.a 5 1
1205.2.a.b 11
1205.2.a.c 15
1205.2.a.d 25
1205.2.a.e 25
1205.2.b \(\chi_{1205}(724, \cdot)\) 1205.2.b.a 4 1
1205.2.b.b 4
1205.2.b.c 46
1205.2.b.d 66
1205.2.c \(\chi_{1205}(1204, \cdot)\) n/a 120 1
1205.2.d \(\chi_{1205}(481, \cdot)\) 1205.2.d.a 6 1
1205.2.d.b 34
1205.2.d.c 42
1205.2.e \(\chi_{1205}(256, \cdot)\) n/a 160 2
1205.2.f \(\chi_{1205}(546, \cdot)\) n/a 164 2
1205.2.k \(\chi_{1205}(64, \cdot)\) n/a 240 2
1205.2.l \(\chi_{1205}(91, \cdot)\) n/a 328 4
1205.2.m \(\chi_{1205}(16, \cdot)\) n/a 160 2
1205.2.n \(\chi_{1205}(739, \cdot)\) n/a 240 2
1205.2.o \(\chi_{1205}(979, \cdot)\) n/a 240 2
1205.2.q \(\chi_{1205}(249, \cdot)\) n/a 472 4
1205.2.r \(\chi_{1205}(211, \cdot)\) n/a 328 4
1205.2.t \(\chi_{1205}(154, \cdot)\) n/a 480 4
1205.2.u \(\chi_{1205}(339, \cdot)\) n/a 480 4
1205.2.v \(\chi_{1205}(36, \cdot)\) n/a 328 4
1205.2.w \(\chi_{1205}(4, \cdot)\) n/a 480 4
1205.2.bb \(\chi_{1205}(181, \cdot)\) n/a 320 4
1205.2.bc \(\chi_{1205}(231, \cdot)\) n/a 640 8
1205.2.bd \(\chi_{1205}(352, \cdot)\) n/a 952 8
1205.2.be \(\chi_{1205}(197, \cdot)\) n/a 952 8
1205.2.bh \(\chi_{1205}(6, \cdot)\) n/a 656 8
1205.2.bm \(\chi_{1205}(729, \cdot)\) n/a 960 8
1205.2.bo \(\chi_{1205}(121, \cdot)\) n/a 640 8
1205.2.bp \(\chi_{1205}(209, \cdot)\) n/a 944 8
1205.2.br \(\chi_{1205}(81, \cdot)\) n/a 640 8
1205.2.bs \(\chi_{1205}(24, \cdot)\) n/a 960 8
1205.2.bt \(\chi_{1205}(299, \cdot)\) n/a 960 8
1205.2.bv \(\chi_{1205}(41, \cdot)\) n/a 1312 16
1205.2.bw \(\chi_{1205}(79, \cdot)\) n/a 1888 16
1205.2.ca \(\chi_{1205}(38, \cdot)\) n/a 1904 16
1205.2.cb \(\chi_{1205}(22, \cdot)\) n/a 1904 16
1205.2.cc \(\chi_{1205}(9, \cdot)\) n/a 1920 16
1205.2.ch \(\chi_{1205}(96, \cdot)\) n/a 1280 16
1205.2.ck \(\chi_{1205}(33, \cdot)\) n/a 3808 32
1205.2.cl \(\chi_{1205}(17, \cdot)\) n/a 3808 32
1205.2.cn \(\chi_{1205}(29, \cdot)\) n/a 3776 32
1205.2.co \(\chi_{1205}(161, \cdot)\) n/a 2560 32
1205.2.cq \(\chi_{1205}(52, \cdot)\) n/a 7616 64
1205.2.cr \(\chi_{1205}(7, \cdot)\) n/a 7616 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1205)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)\(^{\oplus 2}\)