Properties

Label 675.2.n
Level 675
Weight 2
Character orbit n
Rep. character \(\chi_{675}(109,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 160
Newform subspaces 2
Sturm bound 180
Trace bound 10

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 675.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

Total New Old
Modular forms 384 160 224
Cusp forms 336 160 176
Eisenstein series 48 0 48

Trace form

\( 160q + 40q^{4} + O(q^{10}) \) \( 160q + 40q^{4} + 14q^{10} - 28q^{16} - 6q^{19} - 20q^{22} + 14q^{25} - 30q^{28} + 6q^{31} + 40q^{34} - 120q^{37} + 8q^{40} - 8q^{46} - 180q^{49} + 50q^{52} + 36q^{55} + 60q^{58} + 60q^{61} + 40q^{64} - 20q^{67} - 156q^{70} + 20q^{73} + 80q^{76} - 44q^{79} - 8q^{85} - 70q^{88} + 2q^{91} + 102q^{94} - 70q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
675.2.n.a \(80\) \(5.390\) None \(0\) \(0\) \(0\) \(0\)
675.2.n.b \(80\) \(5.390\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database