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Properties

Label 1675.2
Level 1675
Weight 2
Dimension 102034
Nonzero newspaces 24
Sturm bound 448800
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1675 = 5^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(448800\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1675))\).

Total New Old
Modular forms 114048 104698 9350
Cusp forms 110353 102034 8319
Eisenstein series 3695 2664 1031

Trace form

\( 102034 q - 415 q^{2} - 417 q^{3} - 423 q^{4} - 518 q^{5} - 681 q^{6} - 425 q^{7} - 439 q^{8} - 435 q^{9} + O(q^{10}) \) \( 102034 q - 415 q^{2} - 417 q^{3} - 423 q^{4} - 518 q^{5} - 681 q^{6} - 425 q^{7} - 439 q^{8} - 435 q^{9} - 538 q^{10} - 681 q^{11} - 465 q^{12} - 437 q^{13} - 457 q^{14} - 548 q^{15} - 687 q^{16} - 425 q^{17} - 437 q^{18} - 409 q^{19} - 508 q^{20} - 681 q^{21} - 401 q^{22} - 417 q^{23} - 389 q^{24} - 498 q^{25} - 1341 q^{26} - 429 q^{27} - 401 q^{28} - 429 q^{29} - 548 q^{30} - 681 q^{31} - 465 q^{32} - 465 q^{33} - 467 q^{34} - 568 q^{35} - 727 q^{36} - 475 q^{37} - 469 q^{38} - 441 q^{39} - 558 q^{40} - 701 q^{41} - 401 q^{42} - 417 q^{43} - 437 q^{44} - 478 q^{45} - 681 q^{46} - 425 q^{47} - 357 q^{48} - 413 q^{49} - 478 q^{50} - 1321 q^{51} - 429 q^{52} - 460 q^{53} - 488 q^{54} - 548 q^{55} - 911 q^{56} - 486 q^{57} - 581 q^{58} - 495 q^{59} - 508 q^{60} - 833 q^{61} - 447 q^{62} - 580 q^{63} - 773 q^{64} - 538 q^{65} - 1026 q^{66} - 513 q^{67} - 982 q^{68} - 527 q^{69} - 588 q^{70} - 853 q^{71} - 789 q^{72} - 620 q^{73} - 483 q^{74} - 548 q^{75} - 1617 q^{76} - 507 q^{77} - 617 q^{78} - 566 q^{79} - 538 q^{80} - 846 q^{81} - 520 q^{82} - 390 q^{83} - 501 q^{84} - 458 q^{85} - 681 q^{86} - 389 q^{87} - 369 q^{88} - 339 q^{89} - 478 q^{90} - 681 q^{91} - 465 q^{92} - 405 q^{93} - 377 q^{94} - 548 q^{95} - 721 q^{96} - 325 q^{97} - 431 q^{98} - 461 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1675))\)

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
1675.2.a \(\chi_{1675}(1, \cdot)\) 1675.2.a.a 1 1
1675.2.a.b 1
1675.2.a.c 1
1675.2.a.d 1
1675.2.a.e 2
1675.2.a.f 2
1675.2.a.g 2
1675.2.a.h 2
1675.2.a.i 7
1675.2.a.j 8
1675.2.a.k 8
1675.2.a.l 11
1675.2.a.m 13
1675.2.a.n 13
1675.2.a.o 16
1675.2.a.p 16
1675.2.c \(\chi_{1675}(1274, \cdot)\) 1675.2.c.a 2 1
1675.2.c.b 2
1675.2.c.c 2
1675.2.c.d 4
1675.2.c.e 4
1675.2.c.f 4
1675.2.c.g 4
1675.2.c.h 14
1675.2.c.i 16
1675.2.c.j 22
1675.2.c.k 26
1675.2.e \(\chi_{1675}(1101, \cdot)\) n/a 210 2
1675.2.f \(\chi_{1675}(468, \cdot)\) n/a 200 2
1675.2.h \(\chi_{1675}(336, \cdot)\) n/a 664 4
1675.2.j \(\chi_{1675}(699, \cdot)\) n/a 200 2
1675.2.m \(\chi_{1675}(269, \cdot)\) n/a 656 4
1675.2.o \(\chi_{1675}(76, \cdot)\) n/a 1040 10
1675.2.q \(\chi_{1675}(432, \cdot)\) n/a 400 4
1675.2.r \(\chi_{1675}(96, \cdot)\) n/a 1344 8
1675.2.t \(\chi_{1675}(133, \cdot)\) n/a 1344 8
1675.2.v \(\chi_{1675}(24, \cdot)\) n/a 1000 10
1675.2.y \(\chi_{1675}(29, \cdot)\) n/a 1344 8
1675.2.ba \(\chi_{1675}(26, \cdot)\) n/a 2100 20
1675.2.bc \(\chi_{1675}(43, \cdot)\) n/a 2000 20
1675.2.bd \(\chi_{1675}(81, \cdot)\) n/a 6720 40
1675.2.be \(\chi_{1675}(38, \cdot)\) n/a 2688 16
1675.2.bh \(\chi_{1675}(49, \cdot)\) n/a 2000 20
1675.2.bk \(\chi_{1675}(9, \cdot)\) n/a 6720 40
1675.2.bm \(\chi_{1675}(7, \cdot)\) n/a 4000 40
1675.2.bo \(\chi_{1675}(6, \cdot)\) n/a 13440 80
1675.2.bp \(\chi_{1675}(3, \cdot)\) n/a 13440 80
1675.2.bs \(\chi_{1675}(4, \cdot)\) n/a 13440 80
1675.2.bv \(\chi_{1675}(2, \cdot)\) n/a 26880 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1675))\)\(^{\oplus 1}\)