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Properties

Label 176.6
Level 176
Weight 6
Dimension 2615
Nonzero newspaces 8
Sturm bound 11520
Trace bound 2

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Defining parameters

Level: \( N \) = \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(11520\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(176))\).

Total New Old
Modular forms 4940 2695 2245
Cusp forms 4660 2615 2045
Eisenstein series 280 80 200

Trace form

\( 2615 q - 16 q^{2} + 5 q^{3} + 28 q^{4} + 19 q^{5} - 244 q^{6} - 239 q^{7} - 508 q^{8} - 121 q^{9} + O(q^{10}) \) \( 2615 q - 16 q^{2} + 5 q^{3} + 28 q^{4} + 19 q^{5} - 244 q^{6} - 239 q^{7} - 508 q^{8} - 121 q^{9} + 852 q^{10} + 1255 q^{11} - 48 q^{12} - 141 q^{13} + 180 q^{14} - 7863 q^{15} + 1724 q^{16} + 1171 q^{17} + 6256 q^{18} + 12469 q^{19} - 5964 q^{20} - 2150 q^{21} - 4440 q^{22} - 7870 q^{23} - 16756 q^{24} - 4289 q^{25} - 14756 q^{26} - 3679 q^{27} + 14652 q^{28} - 413 q^{29} + 60868 q^{30} + 20113 q^{31} + 47964 q^{32} - 19821 q^{33} + 3440 q^{34} + 18731 q^{35} - 13804 q^{36} + 27839 q^{37} - 106516 q^{38} + 34837 q^{39} - 150564 q^{40} - 64885 q^{41} - 66820 q^{42} - 67292 q^{43} + 40104 q^{44} - 67706 q^{45} + 185044 q^{46} - 49901 q^{47} + 295964 q^{48} + 143163 q^{49} + 170080 q^{50} + 129005 q^{51} - 183164 q^{52} - 50017 q^{53} - 417364 q^{54} + 19939 q^{55} - 382296 q^{56} - 264681 q^{57} - 213572 q^{58} + 77869 q^{59} + 308716 q^{60} + 202579 q^{61} + 547724 q^{62} + 35400 q^{63} + 567532 q^{64} + 60470 q^{65} + 153336 q^{66} + 162950 q^{67} - 267444 q^{68} - 152704 q^{69} - 488200 q^{70} + 2811 q^{71} - 219608 q^{72} - 59677 q^{73} - 642416 q^{74} - 451971 q^{75} - 972444 q^{76} - 564269 q^{77} - 250640 q^{78} - 200541 q^{79} + 457912 q^{80} + 114771 q^{81} + 426212 q^{82} - 27481 q^{83} + 786764 q^{84} + 1031183 q^{85} + 201284 q^{86} + 337126 q^{87} + 1803572 q^{88} + 346014 q^{89} + 1279996 q^{90} + 763077 q^{91} + 794012 q^{92} - 45977 q^{93} + 302364 q^{94} - 115429 q^{95} - 315564 q^{96} - 1015893 q^{97} - 1603108 q^{98} - 348787 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)

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
176.6.a \(\chi_{176}(1, \cdot)\) 176.6.a.a 1 1
176.6.a.b 1
176.6.a.c 1
176.6.a.d 1
176.6.a.e 1
176.6.a.f 2
176.6.a.g 2
176.6.a.h 2
176.6.a.i 3
176.6.a.j 3
176.6.a.k 4
176.6.a.l 4
176.6.c \(\chi_{176}(89, \cdot)\) None 0 1
176.6.e \(\chi_{176}(175, \cdot)\) 176.6.e.a 2 1
176.6.e.b 4
176.6.e.c 8
176.6.e.d 16
176.6.g \(\chi_{176}(87, \cdot)\) None 0 1
176.6.i \(\chi_{176}(43, \cdot)\) n/a 236 2
176.6.j \(\chi_{176}(45, \cdot)\) n/a 200 2
176.6.m \(\chi_{176}(49, \cdot)\) n/a 116 4
176.6.o \(\chi_{176}(7, \cdot)\) None 0 4
176.6.q \(\chi_{176}(63, \cdot)\) n/a 120 4
176.6.s \(\chi_{176}(9, \cdot)\) None 0 4
176.6.w \(\chi_{176}(5, \cdot)\) n/a 944 8
176.6.x \(\chi_{176}(19, \cdot)\) n/a 944 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(176)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)