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Properties

Label 3150.3.do
Level $3150$
Weight $3$
Character orbit 3150.do
Rep. character $\chi_{3150}(241,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3840$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.do (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

Total New Old
Modular forms 11584 3840 7744
Cusp forms 11456 3840 7616
Eisenstein series 128 0 128

Trace form

\( 3840 q - 1920 q^{4} + O(q^{10}) \) \( 3840 q - 1920 q^{4} + 70 q^{15} - 3840 q^{16} - 108 q^{17} + 32 q^{18} - 60 q^{21} + 48 q^{23} + 72 q^{27} + 56 q^{30} + 66 q^{35} - 340 q^{39} + 128 q^{42} - 384 q^{45} + 96 q^{50} + 240 q^{51} + 360 q^{53} - 184 q^{57} + 48 q^{58} - 20 q^{60} - 482 q^{63} - 7680 q^{64} - 132 q^{65} + 864 q^{68} + 630 q^{69} - 192 q^{70} - 540 q^{71} + 64 q^{72} - 342 q^{75} - 528 q^{77} - 256 q^{78} + 240 q^{79} - 40 q^{81} + 2268 q^{83} + 180 q^{84} - 612 q^{87} + 1350 q^{89} - 1440 q^{90} - 144 q^{92} - 488 q^{93} - 1104 q^{95} - 288 q^{98} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)