Properties

Label 45.3.g
Level $45$
Weight $3$
Character orbit 45.g
Rep. character $\chi_{45}(28,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $2$
Sturm bound $18$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

Total New Old
Modular forms 32 12 20
Cusp forms 16 8 8
Eisenstein series 16 4 12

Trace form

\( 8q + 4q^{2} + 4q^{5} - 16q^{7} - 12q^{8} + O(q^{10}) \) \( 8q + 4q^{2} + 4q^{5} - 16q^{7} - 12q^{8} - 16q^{10} - 16q^{11} + 8q^{13} + 56q^{16} + 40q^{17} + 36q^{20} - 80q^{22} - 56q^{23} - 64q^{25} - 88q^{26} + 64q^{28} + 16q^{31} + 76q^{32} + 40q^{35} + 104q^{37} + 96q^{38} + 168q^{40} + 56q^{41} + 32q^{43} - 176q^{46} - 128q^{47} - 164q^{50} - 40q^{52} - 56q^{53} - 224q^{55} - 312q^{58} - 32q^{61} - 88q^{62} + 112q^{65} + 80q^{67} + 104q^{68} + 240q^{70} + 272q^{71} + 296q^{73} + 240q^{76} - 88q^{77} - 164q^{80} + 328q^{82} + 16q^{83} + 272q^{85} + 224q^{86} - 288q^{88} - 416q^{91} - 104q^{92} - 144q^{95} - 40q^{97} + 188q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.3.g.a \(4\) \(1.226\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots\)
45.3.g.b \(4\) \(1.226\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(4\) \(4\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)