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Properties

Label 3150.2.v
Level $3150$
Weight $2$
Character orbit 3150.v
Rep. character $\chi_{3150}(1549,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1536 120 1416
Cusp forms 1344 120 1224
Eisenstein series 192 0 192

Trace form

\( 120 q + 60 q^{4} + O(q^{10}) \) \( 120 q + 60 q^{4} - 8 q^{11} - 12 q^{14} - 60 q^{16} + 12 q^{19} + 8 q^{26} - 40 q^{29} - 4 q^{31} - 16 q^{34} - 88 q^{41} + 8 q^{44} - 8 q^{46} - 48 q^{49} - 12 q^{56} - 20 q^{59} - 56 q^{61} - 120 q^{64} + 72 q^{71} + 12 q^{74} + 24 q^{76} - 44 q^{79} + 24 q^{86} + 116 q^{91} + 12 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)