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Properties

Label 3150.2.bu
Level $3150$
Weight $2$
Character orbit 3150.bu
Rep. character $\chi_{3150}(379,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $304$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 2944 304 2640
Cusp forms 2816 304 2512
Eisenstein series 128 0 128

Trace form

\( 304 q + 76 q^{4} - 16 q^{5} + O(q^{10}) \) \( 304 q + 76 q^{4} - 16 q^{5} + 4 q^{11} - 4 q^{14} - 76 q^{16} + 24 q^{19} - 4 q^{20} + 20 q^{22} - 20 q^{23} - 88 q^{25} + 8 q^{26} - 32 q^{29} - 24 q^{31} + 12 q^{34} - 4 q^{35} + 8 q^{41} - 4 q^{44} - 20 q^{46} - 140 q^{47} - 304 q^{49} + 12 q^{50} + 20 q^{53} + 12 q^{55} + 4 q^{56} + 36 q^{59} - 40 q^{61} + 76 q^{64} + 80 q^{65} + 140 q^{67} - 4 q^{70} - 32 q^{71} + 80 q^{73} + 72 q^{74} + 16 q^{76} + 40 q^{77} + 56 q^{79} + 4 q^{80} + 60 q^{83} + 96 q^{85} + 20 q^{86} + 76 q^{89} - 4 q^{91} + 4 q^{95} + 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)