Properties

Label 45.2.l
Level $45$
Weight $2$
Character orbit 45.l
Rep. character $\chi_{45}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(45, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

Trace form

\( 16q - 6q^{2} - 6q^{3} - 6q^{5} - 2q^{7} + O(q^{10}) \) \( 16q - 6q^{2} - 6q^{3} - 6q^{5} - 2q^{7} - 8q^{10} - 6q^{12} - 2q^{13} - 6q^{15} - 8q^{16} + 36q^{18} + 18q^{20} - 12q^{21} - 10q^{22} + 18q^{23} + 4q^{25} + 18q^{27} - 16q^{28} + 30q^{30} - 4q^{31} + 30q^{32} - 12q^{33} - 48q^{36} + 4q^{37} - 30q^{38} + 6q^{40} - 24q^{41} + 6q^{42} - 2q^{43} - 36q^{45} + 32q^{46} - 12q^{47} - 30q^{48} - 54q^{50} + 36q^{51} - 14q^{52} - 16q^{55} + 36q^{56} - 6q^{57} - 6q^{58} + 18q^{60} + 8q^{61} + 36q^{63} + 66q^{65} + 36q^{66} + 4q^{67} + 42q^{68} + 18q^{70} + 18q^{72} - 8q^{73} + 42q^{75} + 24q^{76} - 6q^{77} - 42q^{78} - 48q^{81} + 32q^{82} - 66q^{83} + 22q^{85} - 48q^{86} - 18q^{87} + 18q^{88} - 66q^{90} - 40q^{91} - 60q^{92} - 18q^{93} - 36q^{95} - 24q^{96} + 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.2.l.a \(16\) \(0.359\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-6\) \(-6\) \(-2\) \(q-\beta _{5}q^{2}+(-1+\beta _{9}-\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots\)