Properties

Label 1175.4
Level 1175
Weight 4
Dimension 151567
Nonzero newspaces 12
Sturm bound 441600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(441600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1175))\).

Total New Old
Modular forms 166888 153411 13477
Cusp forms 164312 151567 12745
Eisenstein series 2576 1844 732

Trace form

\(151567q \) \(\mathstrut -\mathstrut 295q^{2} \) \(\mathstrut -\mathstrut 271q^{3} \) \(\mathstrut -\mathstrut 247q^{4} \) \(\mathstrut -\mathstrut 358q^{5} \) \(\mathstrut -\mathstrut 479q^{6} \) \(\mathstrut -\mathstrut 255q^{7} \) \(\mathstrut -\mathstrut 279q^{8} \) \(\mathstrut -\mathstrut 371q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(151567q \) \(\mathstrut -\mathstrut 295q^{2} \) \(\mathstrut -\mathstrut 271q^{3} \) \(\mathstrut -\mathstrut 247q^{4} \) \(\mathstrut -\mathstrut 358q^{5} \) \(\mathstrut -\mathstrut 479q^{6} \) \(\mathstrut -\mathstrut 255q^{7} \) \(\mathstrut -\mathstrut 279q^{8} \) \(\mathstrut -\mathstrut 371q^{9} \) \(\mathstrut -\mathstrut 308q^{10} \) \(\mathstrut -\mathstrut 319q^{11} \) \(\mathstrut -\mathstrut 215q^{12} \) \(\mathstrut -\mathstrut 431q^{13} \) \(\mathstrut -\mathstrut 375q^{14} \) \(\mathstrut -\mathstrut 368q^{15} \) \(\mathstrut -\mathstrut 191q^{16} \) \(\mathstrut +\mathstrut 465q^{17} \) \(\mathstrut +\mathstrut 989q^{18} \) \(\mathstrut +\mathstrut 361q^{19} \) \(\mathstrut -\mathstrut 708q^{20} \) \(\mathstrut -\mathstrut 879q^{21} \) \(\mathstrut -\mathstrut 2231q^{22} \) \(\mathstrut -\mathstrut 1471q^{23} \) \(\mathstrut -\mathstrut 3139q^{24} \) \(\mathstrut -\mathstrut 1738q^{25} \) \(\mathstrut -\mathstrut 1159q^{26} \) \(\mathstrut -\mathstrut 1759q^{27} \) \(\mathstrut -\mathstrut 1527q^{28} \) \(\mathstrut -\mathstrut 639q^{29} \) \(\mathstrut +\mathstrut 212q^{30} \) \(\mathstrut -\mathstrut 159q^{31} \) \(\mathstrut +\mathstrut 2985q^{32} \) \(\mathstrut +\mathstrut 1897q^{33} \) \(\mathstrut +\mathstrut 2605q^{34} \) \(\mathstrut +\mathstrut 1312q^{35} \) \(\mathstrut -\mathstrut 4319q^{36} \) \(\mathstrut +\mathstrut 843q^{37} \) \(\mathstrut +\mathstrut 1905q^{38} \) \(\mathstrut +\mathstrut 3607q^{39} \) \(\mathstrut +\mathstrut 3752q^{40} \) \(\mathstrut +\mathstrut 1665q^{41} \) \(\mathstrut +\mathstrut 4517q^{42} \) \(\mathstrut +\mathstrut 1711q^{43} \) \(\mathstrut +\mathstrut 1765q^{44} \) \(\mathstrut -\mathstrut 4758q^{45} \) \(\mathstrut +\mathstrut 570q^{46} \) \(\mathstrut -\mathstrut 921q^{47} \) \(\mathstrut -\mathstrut 3030q^{48} \) \(\mathstrut -\mathstrut 4057q^{49} \) \(\mathstrut -\mathstrut 9368q^{50} \) \(\mathstrut -\mathstrut 3329q^{51} \) \(\mathstrut -\mathstrut 7603q^{52} \) \(\mathstrut -\mathstrut 3509q^{53} \) \(\mathstrut -\mathstrut 7599q^{54} \) \(\mathstrut -\mathstrut 2188q^{55} \) \(\mathstrut -\mathstrut 6335q^{56} \) \(\mathstrut -\mathstrut 2775q^{57} \) \(\mathstrut -\mathstrut 215q^{58} \) \(\mathstrut +\mathstrut 5791q^{59} \) \(\mathstrut +\mathstrut 22572q^{60} \) \(\mathstrut +\mathstrut 1349q^{61} \) \(\mathstrut +\mathstrut 21989q^{62} \) \(\mathstrut +\mathstrut 15609q^{63} \) \(\mathstrut +\mathstrut 13093q^{64} \) \(\mathstrut +\mathstrut 3542q^{65} \) \(\mathstrut +\mathstrut 1745q^{66} \) \(\mathstrut -\mathstrut 1215q^{67} \) \(\mathstrut -\mathstrut 7127q^{68} \) \(\mathstrut -\mathstrut 7063q^{69} \) \(\mathstrut -\mathstrut 8748q^{70} \) \(\mathstrut -\mathstrut 3759q^{71} \) \(\mathstrut -\mathstrut 18779q^{72} \) \(\mathstrut -\mathstrut 9551q^{73} \) \(\mathstrut -\mathstrut 19315q^{74} \) \(\mathstrut -\mathstrut 12088q^{75} \) \(\mathstrut -\mathstrut 17981q^{76} \) \(\mathstrut -\mathstrut 18625q^{77} \) \(\mathstrut -\mathstrut 31209q^{78} \) \(\mathstrut -\mathstrut 12963q^{79} \) \(\mathstrut -\mathstrut 12028q^{80} \) \(\mathstrut -\mathstrut 4185q^{81} \) \(\mathstrut +\mathstrut 4976q^{82} \) \(\mathstrut +\mathstrut 13627q^{83} \) \(\mathstrut +\mathstrut 27333q^{84} \) \(\mathstrut +\mathstrut 18922q^{85} \) \(\mathstrut +\mathstrut 16209q^{86} \) \(\mathstrut +\mathstrut 21333q^{87} \) \(\mathstrut +\mathstrut 42309q^{88} \) \(\mathstrut +\mathstrut 21087q^{89} \) \(\mathstrut +\mathstrut 15952q^{90} \) \(\mathstrut +\mathstrut 22251q^{91} \) \(\mathstrut +\mathstrut 25838q^{92} \) \(\mathstrut -\mathstrut 930q^{93} \) \(\mathstrut +\mathstrut 18451q^{94} \) \(\mathstrut -\mathstrut 14356q^{95} \) \(\mathstrut +\mathstrut 13789q^{96} \) \(\mathstrut -\mathstrut 17323q^{97} \) \(\mathstrut -\mathstrut 7256q^{98} \) \(\mathstrut -\mathstrut 12473q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1175))\)

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
1175.4.a \(\chi_{1175}(1, \cdot)\) 1175.4.a.a 3 1
1175.4.a.b 8
1175.4.a.c 8
1175.4.a.d 10
1175.4.a.e 13
1175.4.a.f 15
1175.4.a.g 18
1175.4.a.h 18
1175.4.a.i 28
1175.4.a.j 28
1175.4.a.k 35
1175.4.a.l 35
1175.4.c \(\chi_{1175}(424, \cdot)\) n/a 206 1
1175.4.e \(\chi_{1175}(93, \cdot)\) n/a 428 2
1175.4.g \(\chi_{1175}(236, \cdot)\) n/a 1376 4
1175.4.i \(\chi_{1175}(189, \cdot)\) n/a 1384 4
1175.4.l \(\chi_{1175}(187, \cdot)\) n/a 2864 8
1175.4.m \(\chi_{1175}(51, \cdot)\) n/a 4950 22
1175.4.o \(\chi_{1175}(24, \cdot)\) n/a 4708 22
1175.4.r \(\chi_{1175}(43, \cdot)\) n/a 9416 44
1175.4.s \(\chi_{1175}(6, \cdot)\) n/a 31504 88
1175.4.u \(\chi_{1175}(4, \cdot)\) n/a 31504 88
1175.4.w \(\chi_{1175}(13, \cdot)\) n/a 63008 176

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(235))\)\(^{\oplus 2}\)