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Properties

Label 1075.2
Level 1075
Weight 2
Dimension 41696
Nonzero newspaces 24
Sturm bound 184800
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(184800\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1075))\).

Total New Old
Modular forms 47376 43376 4000
Cusp forms 45025 41696 3329
Eisenstein series 2351 1680 671

Trace form

\( 41696 q - 259 q^{2} - 261 q^{3} - 267 q^{4} - 326 q^{5} - 429 q^{6} - 269 q^{7} - 283 q^{8} - 279 q^{9} + O(q^{10}) \) \( 41696 q - 259 q^{2} - 261 q^{3} - 267 q^{4} - 326 q^{5} - 429 q^{6} - 269 q^{7} - 283 q^{8} - 279 q^{9} - 346 q^{10} - 429 q^{11} - 309 q^{12} - 281 q^{13} - 301 q^{14} - 356 q^{15} - 435 q^{16} - 269 q^{17} - 281 q^{18} - 253 q^{19} - 316 q^{20} - 429 q^{21} - 245 q^{22} - 261 q^{23} - 233 q^{24} - 306 q^{25} - 849 q^{26} - 273 q^{27} - 245 q^{28} - 273 q^{29} - 356 q^{30} - 436 q^{31} - 351 q^{32} - 351 q^{33} - 374 q^{34} - 376 q^{35} - 587 q^{36} - 361 q^{37} - 397 q^{38} - 334 q^{39} - 366 q^{40} - 470 q^{41} - 350 q^{42} - 372 q^{43} - 638 q^{44} - 286 q^{45} - 513 q^{46} - 290 q^{47} - 369 q^{48} - 306 q^{49} - 286 q^{50} - 871 q^{51} - 341 q^{52} - 313 q^{53} - 296 q^{54} - 356 q^{55} - 503 q^{56} - 260 q^{57} - 293 q^{58} - 273 q^{59} - 316 q^{60} - 449 q^{61} - 225 q^{62} - 281 q^{63} - 287 q^{64} - 346 q^{65} - 477 q^{66} - 309 q^{67} - 265 q^{68} - 347 q^{69} - 396 q^{70} - 511 q^{71} - 513 q^{72} - 363 q^{73} - 408 q^{74} - 356 q^{75} - 1008 q^{76} - 411 q^{77} - 602 q^{78} - 417 q^{79} - 346 q^{80} - 663 q^{81} - 475 q^{82} - 285 q^{83} - 721 q^{84} - 266 q^{85} - 603 q^{86} - 716 q^{87} - 423 q^{88} - 267 q^{89} - 286 q^{90} - 513 q^{91} - 519 q^{92} - 417 q^{93} - 389 q^{94} - 356 q^{95} - 742 q^{96} - 295 q^{97} - 422 q^{98} - 452 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1075))\)

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
1075.2.a \(\chi_{1075}(1, \cdot)\) 1075.2.a.a 1 1
1075.2.a.b 1
1075.2.a.c 1
1075.2.a.d 1
1075.2.a.e 1
1075.2.a.f 1
1075.2.a.g 1
1075.2.a.h 1
1075.2.a.i 2
1075.2.a.j 3
1075.2.a.k 3
1075.2.a.l 3
1075.2.a.m 5
1075.2.a.n 5
1075.2.a.o 5
1075.2.a.p 6
1075.2.a.q 6
1075.2.a.r 6
1075.2.a.s 7
1075.2.a.t 7
1075.2.b \(\chi_{1075}(474, \cdot)\) 1075.2.b.a 2 1
1075.2.b.b 2
1075.2.b.c 2
1075.2.b.d 2
1075.2.b.e 2
1075.2.b.f 4
1075.2.b.g 6
1075.2.b.h 10
1075.2.b.i 10
1075.2.b.j 12
1075.2.b.k 12
1075.2.e \(\chi_{1075}(251, \cdot)\) n/a 134 2
1075.2.g \(\chi_{1075}(257, \cdot)\) n/a 128 2
1075.2.h \(\chi_{1075}(216, \cdot)\) n/a 424 4
1075.2.j \(\chi_{1075}(49, \cdot)\) n/a 128 2
1075.2.l \(\chi_{1075}(176, \cdot)\) n/a 396 6
1075.2.o \(\chi_{1075}(44, \cdot)\) n/a 416 4
1075.2.p \(\chi_{1075}(7, \cdot)\) n/a 256 4
1075.2.t \(\chi_{1075}(274, \cdot)\) n/a 384 6
1075.2.u \(\chi_{1075}(6, \cdot)\) n/a 864 8
1075.2.v \(\chi_{1075}(42, \cdot)\) n/a 864 8
1075.2.x \(\chi_{1075}(101, \cdot)\) n/a 804 12
1075.2.y \(\chi_{1075}(32, \cdot)\) n/a 768 12
1075.2.bb \(\chi_{1075}(79, \cdot)\) n/a 864 8
1075.2.bd \(\chi_{1075}(11, \cdot)\) n/a 2592 24
1075.2.bf \(\chi_{1075}(24, \cdot)\) n/a 768 12
1075.2.bi \(\chi_{1075}(37, \cdot)\) n/a 1728 16
1075.2.bj \(\chi_{1075}(4, \cdot)\) n/a 2592 24
1075.2.bn \(\chi_{1075}(18, \cdot)\) n/a 1536 24
1075.2.bo \(\chi_{1075}(31, \cdot)\) n/a 5184 48
1075.2.bq \(\chi_{1075}(2, \cdot)\) n/a 5184 48
1075.2.bs \(\chi_{1075}(9, \cdot)\) n/a 5184 48
1075.2.bu \(\chi_{1075}(3, \cdot)\) n/a 10368 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 2}\)