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Properties

Label 174.6
Level 174
Weight 6
Dimension 1048
Nonzero newspaces 6
Sturm bound 10080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 174 = 2 \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(10080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(174))\).

Total New Old
Modular forms 4312 1048 3264
Cusp forms 4088 1048 3040
Eisenstein series 224 0 224

Trace form

\( 1048 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + O(q^{10}) \) \( 1048 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + 528 q^{10} + 120 q^{11} + 288 q^{12} + 1316 q^{13} - 1408 q^{14} - 1188 q^{15} - 512 q^{16} + 828 q^{17} - 648 q^{18} - 1912 q^{19} - 7072 q^{20} + 16888 q^{21} + 33856 q^{22} + 30776 q^{23} + 10112 q^{24} - 5934 q^{25} - 21336 q^{26} - 53058 q^{27} - 5632 q^{28} - 90134 q^{29} - 51456 q^{30} - 15776 q^{31} - 2048 q^{32} + 62844 q^{33} + 88712 q^{34} + 193360 q^{35} + 39968 q^{36} + 76332 q^{37} - 10112 q^{38} - 124124 q^{39} - 62336 q^{40} - 38388 q^{41} + 12672 q^{42} - 26632 q^{43} + 1920 q^{44} - 35802 q^{45} - 4800 q^{46} + 145256 q^{47} + 4608 q^{48} + 297694 q^{49} - 9848 q^{50} + 82764 q^{51} + 21056 q^{52} - 3114 q^{53} + 5832 q^{54} - 541264 q^{55} - 22528 q^{56} - 164736 q^{57} - 22296 q^{58} - 208864 q^{59} - 19008 q^{60} - 55308 q^{61} + 28736 q^{62} + 14580 q^{63} - 8192 q^{64} + 437178 q^{65} - 4320 q^{66} + 662040 q^{67} + 13248 q^{68} + 252216 q^{69} + 92928 q^{70} - 107944 q^{71} - 10368 q^{72} - 984954 q^{73} + 67664 q^{74} - 952102 q^{75} - 30592 q^{76} + 21120 q^{77} - 584528 q^{78} - 148816 q^{79} + 33792 q^{80} + 235742 q^{81} - 153552 q^{82} + 12936 q^{83} + 560064 q^{84} - 54648 q^{85} - 106528 q^{86} + 1073426 q^{87} + 7680 q^{88} + 65484 q^{89} + 607808 q^{90} + 231616 q^{91} - 19200 q^{92} - 358208 q^{93} + 157440 q^{94} + 126192 q^{95} + 18432 q^{96} - 613578 q^{97} - 113352 q^{98} - 1607700 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(174))\)

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
174.6.a \(\chi_{174}(1, \cdot)\) 174.6.a.a 2 1
174.6.a.b 2
174.6.a.c 2
174.6.a.d 2
174.6.a.e 3
174.6.a.f 3
174.6.a.g 4
174.6.a.h 4
174.6.d \(\chi_{174}(115, \cdot)\) 174.6.d.a 12 1
174.6.d.b 14
174.6.f \(\chi_{174}(17, \cdot)\) 174.6.f.a 100 2
174.6.g \(\chi_{174}(7, \cdot)\) n/a 144 6
174.6.h \(\chi_{174}(13, \cdot)\) n/a 156 6
174.6.k \(\chi_{174}(11, \cdot)\) n/a 600 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(174))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(174)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 1}\)