↑

Properties

Label 1225.4.k
Level $1225$
Weight $4$
Character orbit 1225.k
Rep. character $\chi_{1225}(324,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $352$
Sturm bound $560$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1225, [\chi])\).

Total New Old
Modular forms 888 368 520
Cusp forms 792 352 440
Eisenstein series 96 16 80

Trace form

\( 352 q + 686 q^{4} - 88 q^{6} + 1602 q^{9} + O(q^{10}) \) \( 352 q + 686 q^{4} - 88 q^{6} + 1602 q^{9} + 42 q^{11} - 2550 q^{16} - 50 q^{19} - 536 q^{24} + 546 q^{26} + 968 q^{29} + 666 q^{31} - 472 q^{34} + 12660 q^{36} + 1056 q^{39} - 1304 q^{41} - 958 q^{44} - 662 q^{46} + 2502 q^{51} - 4042 q^{54} - 3282 q^{59} + 1050 q^{61} - 9452 q^{64} + 2472 q^{66} + 5484 q^{69} - 5304 q^{71} + 2804 q^{74} + 5116 q^{76} + 4230 q^{79} - 12080 q^{81} - 6526 q^{86} - 8254 q^{89} - 4930 q^{94} + 1846 q^{96} + 29328 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

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