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Properties

Label 33.7
Level 33
Weight 7
Dimension 168
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(33))\).

Total New Old
Modular forms 260 184 76
Cusp forms 220 168 52
Eisenstein series 40 16 24

Trace form

\( 168 q + 49 q^{3} - 138 q^{4} + 395 q^{6} + 1282 q^{7} - 3200 q^{8} - 3543 q^{9} + O(q^{10}) \) \( 168 q + 49 q^{3} - 138 q^{4} + 395 q^{6} + 1282 q^{7} - 3200 q^{8} - 3543 q^{9} - 20 q^{10} + 3200 q^{11} + 13686 q^{12} + 2578 q^{13} - 21310 q^{14} + 1335 q^{15} + 4398 q^{16} - 7280 q^{17} + 6245 q^{18} - 26546 q^{19} - 56050 q^{20} - 15454 q^{21} + 81890 q^{22} + 49400 q^{23} + 46965 q^{24} + 53700 q^{25} + 13250 q^{26} + 47761 q^{27} - 220652 q^{28} - 128800 q^{29} + 47890 q^{30} + 26026 q^{31} - 88455 q^{33} + 355300 q^{34} + 380480 q^{35} - 136157 q^{36} + 160402 q^{37} - 289250 q^{38} - 272961 q^{39} - 763580 q^{40} - 528360 q^{41} - 200280 q^{42} - 85512 q^{43} + 1111110 q^{44} + 263050 q^{45} + 1429200 q^{46} + 658640 q^{47} + 642334 q^{48} - 140824 q^{49} - 679470 q^{50} - 296675 q^{51} - 2210888 q^{52} - 1355680 q^{53} - 2417370 q^{54} - 542890 q^{55} + 1423240 q^{56} + 385197 q^{57} + 3401060 q^{58} + 775200 q^{59} + 2573030 q^{60} + 258706 q^{61} - 453280 q^{62} + 1528623 q^{63} - 1330058 q^{64} - 510410 q^{66} - 1316328 q^{67} - 842240 q^{68} - 1747840 q^{69} - 568340 q^{70} - 4275200 q^{71} - 4911080 q^{72} - 109382 q^{73} + 2051950 q^{74} + 3957175 q^{75} + 5591676 q^{76} + 2332200 q^{77} + 5454200 q^{78} - 230366 q^{79} + 1175230 q^{80} + 2277273 q^{81} - 3144910 q^{82} - 4816400 q^{83} - 6585166 q^{84} - 7446250 q^{85} - 3074800 q^{86} - 2618010 q^{87} - 2358250 q^{88} + 644200 q^{89} - 3638670 q^{90} + 6320502 q^{91} + 2450750 q^{92} + 11349903 q^{93} + 25104860 q^{94} + 14355680 q^{95} + 14797260 q^{96} + 5406862 q^{97} - 2714225 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.7.b \(\chi_{33}(23, \cdot)\) 33.7.b.a 20 1
33.7.c \(\chi_{33}(10, \cdot)\) 33.7.c.a 12 1
33.7.g \(\chi_{33}(7, \cdot)\) 33.7.g.a 48 4
33.7.h \(\chi_{33}(5, \cdot)\) 33.7.h.a 88 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)