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Properties

Label 3.17.b
Level 3
Weight 17
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(3, [\chi])\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.17.b.a \(4\) \(4.870\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(-2052\) \(0\) \(-3141544\) \(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)