Properties

Label 2450.2.p
Level $2450$
Weight $2$
Character orbit 2450.p
Rep. character $\chi_{2450}(607,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Sturm bound $840$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 1872 240 1632
Cusp forms 1488 240 1248
Eisenstein series 384 0 384

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 40 q^{11} + 120 q^{16} - 36 q^{17} - 16 q^{18} - 24 q^{22} - 4 q^{23} + 24 q^{26} + 48 q^{31} + 48 q^{33} - 192 q^{36} - 4 q^{37} + 24 q^{38} + 8 q^{43} - 16 q^{46} + 12 q^{47} - 32 q^{51} + 20 q^{53} + 8 q^{57} + 8 q^{58} + 96 q^{61} + 48 q^{67} - 36 q^{68} + 32 q^{71} - 16 q^{72} - 12 q^{73} + 72 q^{81} - 48 q^{82} + 40 q^{86} - 24 q^{87} - 12 q^{88} + 8 q^{92} + 52 q^{93} + 24 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)