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Properties

Label 354.4
Level 354
Weight 4
Dimension 2608
Nonzero newspaces 4
Sturm bound 27840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(27840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(354))\).

Total New Old
Modular forms 10672 2608 8064
Cusp forms 10208 2608 7600
Eisenstein series 464 0 464

Trace form

\( 2608 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + O(q^{10}) \) \( 2608 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + 24 q^{10} - 24 q^{11} + 24 q^{12} - 76 q^{13} - 64 q^{14} + 36 q^{15} - 32 q^{16} + 252 q^{17} + 36 q^{18} - 40 q^{19} - 48 q^{20} - 96 q^{21} + 48 q^{22} - 336 q^{23} - 48 q^{24} + 178 q^{25} + 152 q^{26} + 54 q^{27} + 128 q^{28} - 60 q^{29} - 72 q^{30} + 176 q^{31} + 64 q^{32} + 72 q^{33} - 504 q^{34} + 192 q^{35} - 72 q^{36} - 508 q^{37} + 80 q^{38} + 228 q^{39} + 96 q^{40} - 84 q^{41} + 192 q^{42} + 104 q^{43} - 96 q^{44} - 7300 q^{45} - 10696 q^{46} - 8392 q^{47} + 96 q^{48} - 7250 q^{49} - 3604 q^{50} - 292 q^{51} + 1552 q^{52} + 6100 q^{53} + 7606 q^{54} + 15864 q^{55} - 256 q^{56} + 16360 q^{57} + 6848 q^{58} + 14116 q^{59} + 9888 q^{60} + 13140 q^{61} + 4984 q^{62} + 11308 q^{63} - 128 q^{64} + 5112 q^{65} + 262 q^{66} - 5016 q^{67} - 2704 q^{68} - 11056 q^{69} - 17552 q^{70} - 24320 q^{71} + 144 q^{72} - 18068 q^{73} - 20096 q^{74} - 12946 q^{75} - 160 q^{76} + 384 q^{77} - 456 q^{78} + 1040 q^{79} - 192 q^{80} - 162 q^{81} + 168 q^{82} + 984 q^{83} - 384 q^{84} + 1512 q^{85} - 208 q^{86} + 180 q^{87} + 192 q^{88} - 1620 q^{89} + 216 q^{90} + 1216 q^{91} - 1344 q^{92} - 528 q^{93} - 384 q^{94} - 240 q^{95} - 192 q^{96} - 2308 q^{97} - 348 q^{98} - 216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(354))\)

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
354.4.a \(\chi_{354}(1, \cdot)\) 354.4.a.a 2 1
354.4.a.b 2
354.4.a.c 2
354.4.a.d 3
354.4.a.e 3
354.4.a.f 3
354.4.a.g 3
354.4.a.h 4
354.4.a.i 6
354.4.c \(\chi_{354}(353, \cdot)\) 354.4.c.a 30 1
354.4.c.b 30
354.4.e \(\chi_{354}(7, \cdot)\) n/a 840 28
354.4.g \(\chi_{354}(11, \cdot)\) n/a 1680 28

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

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