Properties

Label 3.17
Level 3
Weight 17
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(3))\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\( 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9} + O(q^{10}) \) \( 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9} - 18646560 q^{10} + 572494608 q^{12} - 1580730424 q^{13} + 6829958880 q^{15} - 14561268608 q^{16} + 42304978080 q^{18} - 56117116360 q^{19} + 124455437064 q^{21} - 173545812000 q^{22} + 100515572352 q^{24} - 8074048700 q^{25} - 317983667652 q^{27} + 746852001056 q^{28} - 1762329117600 q^{30} + 2471781156248 q^{31} - 3610697951520 q^{33} + 2721261612672 q^{34} - 1219654126512 q^{36} + 370563213896 q^{37} + 7022170227384 q^{39} - 11795287092480 q^{40} + 27587883687840 q^{42} - 28065022062664 q^{43} + 18795326443200 q^{45} - 43994579504832 q^{46} + 41041959355008 q^{48} + 29478262537164 q^{49} - 82841575222656 q^{51} + 42193089120416 q^{52} - 107063660756304 q^{54} + 290253653236800 q^{55} - 335129108488344 q^{57} + 8796421982880 q^{58} + 56126440892160 q^{60} + 362269793083208 q^{61} - 266698363786344 q^{63} - 653949742779392 q^{64} + 1332768950045280 q^{66} - 26774405363464 q^{67} + 58823173290816 q^{69} - 2292362286177600 q^{70} + 2397649754476800 q^{72} + 317628887539976 q^{73} - 1511365865026500 q^{75} - 2008642200508384 q^{76} + 1538179445855520 q^{78} + 4794017165184920 q^{79} - 6444192852054396 q^{81} + 1589112481320000 q^{82} - 1210523902199136 q^{84} + 7999994092573440 q^{85} - 8850169595242080 q^{87} - 3370289894104320 q^{88} + 3549134645307360 q^{90} + 9328538231657008 q^{91} - 2064207396761784 q^{93} - 12859596129667968 q^{94} + 15507630559798272 q^{96} - 13833795002601784 q^{97} + 18943177097338560 q^{99} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(3))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.17.b \(\chi_{3}(2, \cdot)\) 3.17.b.a 4 1