Properties

Label 44.4.a
Level $44$
Weight $4$
Character orbit 44.a
Rep. character $\chi_{44}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 44.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(44))\).

Total New Old
Modular forms 21 3 18
Cusp forms 15 3 12
Eisenstein series 6 0 6

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

\(2\)\(11\)FrickeDim
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3 q + 4 q^{3} + 4 q^{5} - 16 q^{7} + 33 q^{9} + O(q^{10}) \) \( 3 q + 4 q^{3} + 4 q^{5} - 16 q^{7} + 33 q^{9} + 11 q^{11} + 30 q^{13} + 36 q^{15} - 114 q^{17} - 84 q^{19} - 116 q^{21} - 92 q^{23} - 217 q^{25} + 496 q^{27} - 122 q^{29} + 108 q^{31} + 154 q^{33} + 528 q^{35} + 312 q^{37} - 456 q^{39} - 790 q^{41} + 340 q^{43} - 230 q^{45} - 536 q^{47} + 1443 q^{49} - 1144 q^{51} + 354 q^{53} + 198 q^{55} + 1504 q^{57} + 804 q^{59} - 1010 q^{61} - 2392 q^{63} - 388 q^{65} + 204 q^{67} - 1786 q^{69} + 1604 q^{71} - 814 q^{73} - 788 q^{75} + 396 q^{77} + 2552 q^{79} + 1467 q^{81} - 1204 q^{83} - 1008 q^{85} + 1336 q^{87} - 496 q^{89} - 880 q^{91} + 3318 q^{93} - 232 q^{95} + 1204 q^{97} + 407 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(44))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
44.4.a.a 44.a 1.a $1$ $2.596$ \(\Q\) None \(0\) \(-5\) \(-7\) \(-26\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}-7q^{5}-26q^{7}-2q^{9}-11q^{11}+\cdots\)
44.4.a.b 44.a 1.a $2$ $2.596$ \(\Q(\sqrt{97}) \) None \(0\) \(9\) \(11\) \(10\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(5-\beta )q^{3}+(5+\beta )q^{5}+(2+6\beta )q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(44))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(44)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)