↑

Properties

Label 3528.2.fn
Level $3528$
Weight $2$
Character orbit 3528.fn
Rep. character $\chi_{3528}(451,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3336$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.fn (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 8160 3384 4776
Cusp forms 7968 3336 4632
Eisenstein series 192 48 144

Trace form

\( 3336 q + 13 q^{2} - 13 q^{4} + 16 q^{8} + O(q^{10}) \) \( 3336 q + 13 q^{2} - 13 q^{4} + 16 q^{8} - 20 q^{10} + 26 q^{11} - 25 q^{14} - 9 q^{16} + 22 q^{17} - 36 q^{19} + 14 q^{20} - 2 q^{22} + 244 q^{25} - 10 q^{26} + 42 q^{28} + 13 q^{32} + 70 q^{34} + 22 q^{35} - 14 q^{38} - 52 q^{40} + 28 q^{41} - 20 q^{43} + 64 q^{44} - 14 q^{46} - 32 q^{49} - 64 q^{50} + 46 q^{52} - 40 q^{56} - 26 q^{59} - 52 q^{64} + 16 q^{65} - 24 q^{67} + 81 q^{68} + 38 q^{70} + 2 q^{73} + 12 q^{74} - 63 q^{76} + 156 q^{80} - 76 q^{82} + 28 q^{83} - 59 q^{86} + 157 q^{88} + 46 q^{89} + 164 q^{91} + 2 q^{92} - 176 q^{94} - 149 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)