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Properties

Label 3009.2.bm
Level $3009$
Weight $2$
Character orbit 3009.bm
Rep. character $\chi_{3009}(5,\cdot)$
Character field $\Q(\zeta_{464})$
Dimension $79744$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.bm (of order \(464\) and degree \(224\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3009 \)
Character field: \(\Q(\zeta_{464})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 81536 81536 0
Cusp forms 79744 79744 0
Eisenstein series 1792 1792 0

Trace form

\( 79744 q - 216 q^{3} - 432 q^{4} - 216 q^{6} - 432 q^{7} - 216 q^{9} + O(q^{10}) \) \( 79744 q - 216 q^{3} - 432 q^{4} - 216 q^{6} - 432 q^{7} - 216 q^{9} - 432 q^{10} - 264 q^{12} - 432 q^{13} - 240 q^{15} - 432 q^{18} - 432 q^{19} - 240 q^{21} - 432 q^{22} - 264 q^{24} - 432 q^{25} - 216 q^{27} - 432 q^{28} - 216 q^{30} - 496 q^{31} - 432 q^{34} - 248 q^{36} - 496 q^{37} - 216 q^{39} - 560 q^{40} - 216 q^{42} - 528 q^{43} - 152 q^{45} - 368 q^{46} - 104 q^{48} - 368 q^{49} - 216 q^{51} - 864 q^{52} - 1808 q^{54} - 368 q^{55} - 248 q^{57} - 832 q^{58} - 656 q^{60} - 432 q^{61} - 264 q^{63} - 560 q^{64} - 168 q^{66} - 432 q^{69} - 496 q^{70} - 152 q^{72} - 432 q^{73} - 312 q^{75} - 432 q^{76} - 424 q^{78} - 496 q^{79} - 328 q^{81} - 432 q^{82} - 528 q^{85} - 120 q^{87} - 304 q^{88} - 296 q^{90} - 432 q^{91} - 88 q^{93} - 368 q^{94} - 312 q^{96} - 432 q^{97} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.