Properties

Label 1003.2
Level 1003
Weight 2
Dimension 40589
Nonzero newspaces 10
Sturm bound 167040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1003 = 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(167040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1003))\).

Total New Old
Modular forms 42688 42301 387
Cusp forms 40833 40589 244
Eisenstein series 1855 1712 143

Trace form

\(40589q \) \(\mathstrut -\mathstrut 399q^{2} \) \(\mathstrut -\mathstrut 402q^{3} \) \(\mathstrut -\mathstrut 411q^{4} \) \(\mathstrut -\mathstrut 408q^{5} \) \(\mathstrut -\mathstrut 426q^{6} \) \(\mathstrut -\mathstrut 414q^{7} \) \(\mathstrut -\mathstrut 435q^{8} \) \(\mathstrut -\mathstrut 429q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(40589q \) \(\mathstrut -\mathstrut 399q^{2} \) \(\mathstrut -\mathstrut 402q^{3} \) \(\mathstrut -\mathstrut 411q^{4} \) \(\mathstrut -\mathstrut 408q^{5} \) \(\mathstrut -\mathstrut 426q^{6} \) \(\mathstrut -\mathstrut 414q^{7} \) \(\mathstrut -\mathstrut 435q^{8} \) \(\mathstrut -\mathstrut 429q^{9} \) \(\mathstrut -\mathstrut 436q^{10} \) \(\mathstrut -\mathstrut 410q^{11} \) \(\mathstrut -\mathstrut 426q^{12} \) \(\mathstrut -\mathstrut 416q^{13} \) \(\mathstrut -\mathstrut 430q^{14} \) \(\mathstrut -\mathstrut 414q^{15} \) \(\mathstrut -\mathstrut 411q^{16} \) \(\mathstrut -\mathstrut 438q^{17} \) \(\mathstrut -\mathstrut 891q^{18} \) \(\mathstrut -\mathstrut 434q^{19} \) \(\mathstrut -\mathstrut 460q^{20} \) \(\mathstrut -\mathstrut 438q^{21} \) \(\mathstrut -\mathstrut 466q^{22} \) \(\mathstrut -\mathstrut 446q^{23} \) \(\mathstrut -\mathstrut 490q^{24} \) \(\mathstrut -\mathstrut 427q^{25} \) \(\mathstrut -\mathstrut 444q^{26} \) \(\mathstrut -\mathstrut 462q^{27} \) \(\mathstrut -\mathstrut 462q^{28} \) \(\mathstrut -\mathstrut 440q^{29} \) \(\mathstrut -\mathstrut 478q^{30} \) \(\mathstrut -\mathstrut 422q^{31} \) \(\mathstrut -\mathstrut 467q^{32} \) \(\mathstrut -\mathstrut 454q^{33} \) \(\mathstrut -\mathstrut 396q^{34} \) \(\mathstrut -\mathstrut 918q^{35} \) \(\mathstrut -\mathstrut 503q^{36} \) \(\mathstrut -\mathstrut 440q^{37} \) \(\mathstrut -\mathstrut 474q^{38} \) \(\mathstrut -\mathstrut 462q^{39} \) \(\mathstrut -\mathstrut 468q^{40} \) \(\mathstrut -\mathstrut 428q^{41} \) \(\mathstrut -\mathstrut 486q^{42} \) \(\mathstrut -\mathstrut 442q^{43} \) \(\mathstrut -\mathstrut 450q^{44} \) \(\mathstrut -\mathstrut 462q^{45} \) \(\mathstrut -\mathstrut 394q^{46} \) \(\mathstrut -\mathstrut 396q^{47} \) \(\mathstrut -\mathstrut 206q^{48} \) \(\mathstrut -\mathstrut 381q^{49} \) \(\mathstrut -\mathstrut 309q^{50} \) \(\mathstrut -\mathstrut 379q^{51} \) \(\mathstrut -\mathstrut 772q^{52} \) \(\mathstrut -\mathstrut 348q^{53} \) \(\mathstrut -\mathstrut 104q^{54} \) \(\mathstrut -\mathstrut 304q^{55} \) \(\mathstrut -\mathstrut 46q^{56} \) \(\mathstrut -\mathstrut 148q^{57} \) \(\mathstrut -\mathstrut 310q^{58} \) \(\mathstrut -\mathstrut 337q^{59} \) \(\mathstrut -\mathstrut 268q^{60} \) \(\mathstrut -\mathstrut 332q^{61} \) \(\mathstrut -\mathstrut 354q^{62} \) \(\mathstrut -\mathstrut 172q^{63} \) \(\mathstrut -\mathstrut 83q^{64} \) \(\mathstrut -\mathstrut 316q^{65} \) \(\mathstrut -\mathstrut 160q^{66} \) \(\mathstrut -\mathstrut 398q^{67} \) \(\mathstrut -\mathstrut 348q^{68} \) \(\mathstrut -\mathstrut 670q^{69} \) \(\mathstrut -\mathstrut 318q^{70} \) \(\mathstrut -\mathstrut 394q^{71} \) \(\mathstrut -\mathstrut 235q^{72} \) \(\mathstrut -\mathstrut 354q^{73} \) \(\mathstrut -\mathstrut 448q^{74} \) \(\mathstrut -\mathstrut 448q^{75} \) \(\mathstrut -\mathstrut 570q^{76} \) \(\mathstrut -\mathstrut 518q^{77} \) \(\mathstrut -\mathstrut 558q^{78} \) \(\mathstrut -\mathstrut 502q^{79} \) \(\mathstrut -\mathstrut 596q^{80} \) \(\mathstrut -\mathstrut 545q^{81} \) \(\mathstrut -\mathstrut 552q^{82} \) \(\mathstrut -\mathstrut 514q^{83} \) \(\mathstrut -\mathstrut 694q^{84} \) \(\mathstrut -\mathstrut 445q^{85} \) \(\mathstrut -\mathstrut 1010q^{86} \) \(\mathstrut -\mathstrut 558q^{87} \) \(\mathstrut -\mathstrut 610q^{88} \) \(\mathstrut -\mathstrut 516q^{89} \) \(\mathstrut -\mathstrut 636q^{90} \) \(\mathstrut -\mathstrut 502q^{91} \) \(\mathstrut -\mathstrut 510q^{92} \) \(\mathstrut -\mathstrut 582q^{93} \) \(\mathstrut -\mathstrut 502q^{94} \) \(\mathstrut -\mathstrut 526q^{95} \) \(\mathstrut -\mathstrut 618q^{96} \) \(\mathstrut -\mathstrut 556q^{97} \) \(\mathstrut -\mathstrut 385q^{98} \) \(\mathstrut -\mathstrut 380q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)

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
1003.2.a \(\chi_{1003}(1, \cdot)\) 1003.2.a.a 1 1
1003.2.a.b 1
1003.2.a.c 1
1003.2.a.d 1
1003.2.a.e 3
1003.2.a.f 4
1003.2.a.g 10
1003.2.a.h 16
1003.2.a.i 18
1003.2.a.j 22
1003.2.d \(\chi_{1003}(237, \cdot)\) 1003.2.d.a 2 1
1003.2.d.b 4
1003.2.d.c 38
1003.2.d.d 44
1003.2.e \(\chi_{1003}(591, \cdot)\) n/a 176 2
1003.2.g \(\chi_{1003}(60, \cdot)\) n/a 344 4
1003.2.i \(\chi_{1003}(58, \cdot)\) n/a 704 8
1003.2.k \(\chi_{1003}(35, \cdot)\) n/a 2240 28
1003.2.l \(\chi_{1003}(16, \cdot)\) n/a 2464 28
1003.2.p \(\chi_{1003}(4, \cdot)\) n/a 4928 56
1003.2.r \(\chi_{1003}(9, \cdot)\) n/a 9856 112
1003.2.t \(\chi_{1003}(6, \cdot)\) n/a 19712 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)