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Properties

Label 180.7
Level 180
Weight 7
Dimension 2166
Nonzero newspaces 12
Sturm bound 12096
Trace bound 3

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Defining parameters

Level: \( N \) = \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(12096\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(180))\).

Total New Old
Modular forms 5344 2218 3126
Cusp forms 5024 2166 2858
Eisenstein series 320 52 268

Trace form

\( 2166 q - 16 q^{2} - 12 q^{3} - 46 q^{4} + 26 q^{5} + 626 q^{6} + 952 q^{7} - 640 q^{8} - 636 q^{9} + O(q^{10}) \) \( 2166 q - 16 q^{2} - 12 q^{3} - 46 q^{4} + 26 q^{5} + 626 q^{6} + 952 q^{7} - 640 q^{8} - 636 q^{9} + 2494 q^{10} + 4324 q^{11} - 10976 q^{12} + 11190 q^{13} - 6060 q^{14} + 12432 q^{15} + 11530 q^{16} + 394 q^{17} - 28744 q^{18} + 32008 q^{19} + 9876 q^{20} - 12044 q^{21} - 49474 q^{22} + 4144 q^{23} + 48162 q^{24} - 228240 q^{25} - 49020 q^{26} + 4656 q^{27} + 45008 q^{28} + 10596 q^{29} - 82284 q^{30} - 95744 q^{31} - 156386 q^{32} + 250104 q^{33} + 93006 q^{34} - 215432 q^{35} + 209130 q^{36} - 69018 q^{37} - 108290 q^{38} - 24104 q^{39} - 176144 q^{40} + 8976 q^{41} - 48272 q^{42} + 29764 q^{43} + 173012 q^{44} + 202326 q^{45} - 82104 q^{46} + 58680 q^{47} + 1143098 q^{48} - 479508 q^{49} + 641806 q^{50} + 111708 q^{51} - 935544 q^{52} + 1262542 q^{53} - 493102 q^{54} - 33888 q^{55} + 213212 q^{56} - 453796 q^{57} + 300704 q^{58} - 2290356 q^{59} + 723316 q^{60} - 1340604 q^{61} - 1505620 q^{62} + 1073888 q^{63} + 2442380 q^{64} - 49924 q^{65} + 970420 q^{66} + 585892 q^{67} - 310922 q^{68} + 975724 q^{69} - 2041854 q^{70} - 927184 q^{71} - 2865990 q^{72} - 1207482 q^{73} - 145428 q^{74} + 227544 q^{75} + 1061398 q^{76} - 858772 q^{77} + 6700820 q^{78} - 1623416 q^{79} + 1425352 q^{80} - 1423116 q^{81} + 2262456 q^{82} + 1378608 q^{83} - 11023964 q^{84} + 1974986 q^{85} - 9059970 q^{86} + 1639672 q^{87} - 1127722 q^{88} + 13394432 q^{89} + 2518404 q^{90} - 1432288 q^{91} + 7477716 q^{92} - 5011868 q^{93} + 4390684 q^{94} - 1884748 q^{95} + 8891000 q^{96} - 10339194 q^{97} + 2268510 q^{98} + 3628888 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(180))\)

We only show spaces with odd 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
180.7.b \(\chi_{180}(89, \cdot)\) 180.7.b.a 12 1
180.7.c \(\chi_{180}(91, \cdot)\) 180.7.c.a 12 1
180.7.c.b 24
180.7.c.c 24
180.7.f \(\chi_{180}(19, \cdot)\) 180.7.f.a 1 1
180.7.f.b 1
180.7.f.c 2
180.7.f.d 4
180.7.f.e 12
180.7.f.f 32
180.7.f.g 36
180.7.g \(\chi_{180}(161, \cdot)\) 180.7.g.a 8 1
180.7.l \(\chi_{180}(37, \cdot)\) 180.7.l.a 6 2
180.7.l.b 12
180.7.l.c 12
180.7.m \(\chi_{180}(107, \cdot)\) n/a 144 2
180.7.o \(\chi_{180}(41, \cdot)\) 180.7.o.a 48 2
180.7.p \(\chi_{180}(79, \cdot)\) n/a 424 2
180.7.s \(\chi_{180}(31, \cdot)\) n/a 288 2
180.7.t \(\chi_{180}(29, \cdot)\) 180.7.t.a 72 2
180.7.u \(\chi_{180}(13, \cdot)\) n/a 144 4
180.7.v \(\chi_{180}(23, \cdot)\) n/a 848 4

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(180)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)