↑

Properties

Label 2450.4.c
Level $2450$
Weight $4$
Character orbit 2450.c
Rep. character $\chi_{2450}(99,\cdot)$
Character field $\Q$
Dimension $184$
Sturm bound $1680$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2450, [\chi])\).

Total New Old
Modular forms 1308 184 1124
Cusp forms 1212 184 1028
Eisenstein series 96 0 96

Trace form

\( 184 q - 736 q^{4} + 4 q^{6} - 1666 q^{9} + O(q^{10}) \) \( 184 q - 736 q^{4} + 4 q^{6} - 1666 q^{9} - 122 q^{11} + 2944 q^{16} - 226 q^{19} - 16 q^{24} + 272 q^{26} - 84 q^{29} - 380 q^{31} - 620 q^{34} + 6664 q^{36} - 728 q^{39} + 1534 q^{41} + 488 q^{44} - 872 q^{46} - 1186 q^{51} - 1108 q^{54} - 1300 q^{59} - 428 q^{61} - 11776 q^{64} + 340 q^{66} - 3260 q^{69} - 1112 q^{71} - 1600 q^{74} + 904 q^{76} + 4612 q^{79} + 16232 q^{81} + 752 q^{86} + 2598 q^{89} + 512 q^{94} + 64 q^{96} + 1180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)