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Properties

Label 354.5
Level 354
Weight 5
Dimension 3476
Nonzero newspaces 4
Sturm bound 34800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(34800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(354))\).

Total New Old
Modular forms 14152 3476 10676
Cusp forms 13688 3476 10212
Eisenstein series 464 0 464

Trace form

\( 3476 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + O(q^{10}) \) \( 3476 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + 192 q^{10} - 96 q^{12} - 200 q^{13} - 576 q^{15} - 256 q^{16} + 576 q^{18} + 1432 q^{19} + 312 q^{21} - 1344 q^{22} + 768 q^{24} - 1348 q^{25} - 2484 q^{27} + 832 q^{28} - 576 q^{30} + 2968 q^{31} + 4032 q^{33} + 2304 q^{34} - 2016 q^{36} - 7496 q^{37} + 600 q^{39} - 1536 q^{40} - 2496 q^{42} + 1048 q^{43} + 63022 q^{45} + 76608 q^{46} + 34452 q^{47} + 768 q^{48} - 28596 q^{49} - 66816 q^{50} - 92984 q^{51} - 45728 q^{52} - 93960 q^{53} - 70384 q^{54} - 113508 q^{55} - 37066 q^{57} - 16320 q^{58} + 27144 q^{59} + 44976 q^{60} + 84592 q^{61} + 50112 q^{62} + 153002 q^{63} + 2048 q^{64} + 197316 q^{65} + 114464 q^{66} + 128608 q^{67} + 41760 q^{68} + 30712 q^{69} - 6144 q^{70} - 81432 q^{71} - 4608 q^{72} - 138620 q^{73} - 200448 q^{74} - 133010 q^{75} - 11456 q^{76} - 4800 q^{78} - 39272 q^{79} - 5508 q^{81} + 27264 q^{82} - 2496 q^{84} + 13824 q^{85} + 48960 q^{87} + 10752 q^{88} - 12096 q^{90} - 5200 q^{91} - 8904 q^{93} - 19200 q^{94} - 6144 q^{96} + 1912 q^{97} - 24192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(354))\)

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
354.5.b \(\chi_{354}(119, \cdot)\) 354.5.b.a 76 1
354.5.d \(\chi_{354}(235, \cdot)\) 354.5.d.a 40 1
354.5.f \(\chi_{354}(13, \cdot)\) n/a 1120 28
354.5.h \(\chi_{354}(5, \cdot)\) n/a 2240 28

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)