Properties

Label 45.4.a
Level $45$
Weight $4$
Character orbit 45.a
Rep. character $\chi_{45}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(45))\).

Total New Old
Modular forms 22 5 17
Cusp forms 14 5 9
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\( 5 q + 36 q^{4} + 5 q^{5} - 58 q^{7} + 36 q^{8} + O(q^{10}) \) \( 5 q + 36 q^{4} + 5 q^{5} - 58 q^{7} + 36 q^{8} - 40 q^{10} - 60 q^{11} + 18 q^{13} - 12 q^{14} + 84 q^{16} - 66 q^{17} - 132 q^{19} + 80 q^{20} + 352 q^{22} + 366 q^{23} + 125 q^{25} - 396 q^{26} - 784 q^{28} - 102 q^{29} + 20 q^{31} - 372 q^{32} - 56 q^{34} + 250 q^{35} + 82 q^{37} + 792 q^{38} - 420 q^{40} - 474 q^{41} + 906 q^{43} + 132 q^{44} + 984 q^{46} + 282 q^{47} + 1097 q^{49} - 1064 q^{52} - 114 q^{53} - 280 q^{55} + 60 q^{56} - 304 q^{58} - 624 q^{59} - 1134 q^{61} - 744 q^{62} - 820 q^{64} + 70 q^{65} - 514 q^{67} - 360 q^{68} + 1200 q^{70} + 204 q^{71} - 2166 q^{73} + 1308 q^{74} - 680 q^{76} + 1536 q^{77} - 1192 q^{79} - 880 q^{80} + 5024 q^{82} - 1650 q^{83} - 370 q^{85} + 1680 q^{86} + 4224 q^{88} - 1206 q^{89} + 1924 q^{91} - 432 q^{92} - 560 q^{94} - 20 q^{95} - 2294 q^{97} - 1632 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(45))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5
45.4.a.a 45.a 1.a $1$ $2.655$ \(\Q\) None \(-5\) \(0\) \(5\) \(-30\) $+$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+5q^{5}-30q^{7}-45q^{8}+\cdots\)
45.4.a.b 45.a 1.a $1$ $2.655$ \(\Q\) None \(-3\) \(0\) \(5\) \(20\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+20q^{7}+21q^{8}+\cdots\)
45.4.a.c 45.a 1.a $1$ $2.655$ \(\Q\) None \(-1\) \(0\) \(-5\) \(-24\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}-24q^{7}+15q^{8}+\cdots\)
45.4.a.d 45.a 1.a $1$ $2.655$ \(\Q\) None \(4\) \(0\) \(5\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}+5q^{5}+6q^{7}+20q^{10}+\cdots\)
45.4.a.e 45.a 1.a $1$ $2.655$ \(\Q\) None \(5\) \(0\) \(-5\) \(-30\) $+$ $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+17q^{4}-5q^{5}-30q^{7}+45q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(45))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(45)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)