Properties

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

Related objects

Downloads

Learn more about

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

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

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into irreducible Hecke orbits

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

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