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Properties

Label 3150.3.dt
Level $3150$
Weight $3$
Character orbit 3150.dt
Rep. character $\chi_{3150}(229,\cdot)$
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.dt (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

\( 3840 q + 1920 q^{4} + O(q^{10}) \) \( 3840 q + 1920 q^{4} - 58 q^{15} - 3840 q^{16} + 60 q^{21} - 8 q^{30} + 6 q^{35} - 340 q^{39} - 384 q^{45} - 240 q^{51} - 44 q^{60} - 550 q^{63} + 7680 q^{64} + 36 q^{65} + 630 q^{69} + 192 q^{70} + 540 q^{71} + 726 q^{75} - 240 q^{77} + 240 q^{79} + 40 q^{81} + 3780 q^{83} + 180 q^{84} + 1350 q^{89} - 864 q^{90} + 240 q^{92} - 48 q^{95} - 160 q^{99} + O(q^{100}) \)

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

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