↑

Properties

Label 2450.2.z
Level $2450$
Weight $2$
Character orbit 2450.z
Rep. character $\chi_{2450}(307,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1008$
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.z (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 5184 1008 4176
Cusp forms 4896 1008 3888
Eisenstein series 288 0 288

Trace form

\( 1008 q - 56 q^{6} - 8 q^{7} + O(q^{10}) \) \( 1008 q - 56 q^{6} - 8 q^{7} - 16 q^{11} + 168 q^{16} - 28 q^{17} - 8 q^{21} + 20 q^{22} - 8 q^{23} + 56 q^{26} + 8 q^{28} + 128 q^{36} + 24 q^{37} + 112 q^{41} + 112 q^{42} + 24 q^{43} + 136 q^{46} + 84 q^{47} + 160 q^{51} + 100 q^{53} + 40 q^{56} - 92 q^{57} + 80 q^{58} - 56 q^{61} + 32 q^{67} - 32 q^{71} - 16 q^{77} + 80 q^{78} + 256 q^{81} - 140 q^{83} + 16 q^{86} + 28 q^{87} + 8 q^{88} - 168 q^{91} - 8 q^{92} - 20 q^{93} + 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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