↑

Properties

Label 2025.2.l
Level $2025$
Weight $2$
Character orbit 2025.l
Rep. character $\chi_{2025}(226,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $324$
Sturm bound $540$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2025, [\chi])\).

Total New Old
Modular forms 1728 360 1368
Cusp forms 1512 324 1188
Eisenstein series 216 36 180

Trace form

\( 324 q - 6 q^{2} + 6 q^{4} + 6 q^{7} - 12 q^{8} + O(q^{10}) \) \( 324 q - 6 q^{2} + 6 q^{4} + 6 q^{7} - 12 q^{8} + 21 q^{11} + 6 q^{13} - 15 q^{14} - 24 q^{16} - 15 q^{17} + 3 q^{19} + 15 q^{22} + 24 q^{23} - 18 q^{26} + 12 q^{28} + 30 q^{29} - 27 q^{31} + 72 q^{32} + 33 q^{34} + 3 q^{37} - 6 q^{38} - 3 q^{41} + 15 q^{43} + 3 q^{44} - 9 q^{46} + 57 q^{47} - 12 q^{49} + 45 q^{52} + 54 q^{53} - 69 q^{56} + 33 q^{58} + 42 q^{59} - 36 q^{61} + 6 q^{62} - 96 q^{64} + 33 q^{67} + 75 q^{68} + 63 q^{71} + 12 q^{73} - 111 q^{74} - 36 q^{76} - 75 q^{77} + 42 q^{79} + 12 q^{82} + 9 q^{83} + 111 q^{86} - 78 q^{88} + 87 q^{89} + 9 q^{92} + 69 q^{94} + 51 q^{97} - 75 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2025, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)