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Properties

Label 46.4.a
Level $46$
Weight $4$
Character orbit 46.a
Rep. character $\chi_{46}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 46.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(46))\).

Total New Old
Modular forms 20 6 14
Cusp forms 16 6 10
Eisenstein series 4 0 4

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

\(2\)\(23\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\( 6 q - 8 q^{3} + 24 q^{4} - 10 q^{5} - 8 q^{6} + 8 q^{7} + 146 q^{9} + O(q^{10}) \) \( 6 q - 8 q^{3} + 24 q^{4} - 10 q^{5} - 8 q^{6} + 8 q^{7} + 146 q^{9} - 20 q^{10} - 34 q^{11} - 32 q^{12} - 112 q^{13} + 40 q^{14} + 4 q^{15} + 96 q^{16} + 28 q^{17} - 128 q^{18} + 38 q^{19} - 40 q^{20} - 260 q^{21} - 188 q^{22} - 32 q^{24} + 78 q^{25} + 192 q^{26} - 404 q^{27} + 32 q^{28} - 276 q^{29} + 480 q^{30} - 156 q^{31} + 948 q^{33} - 520 q^{34} + 544 q^{35} + 584 q^{36} + 294 q^{37} - 436 q^{38} - 444 q^{39} - 80 q^{40} + 484 q^{41} - 64 q^{42} - 366 q^{43} - 136 q^{44} - 326 q^{45} + 92 q^{46} + 1364 q^{47} - 128 q^{48} - 1154 q^{49} + 728 q^{50} - 988 q^{51} - 448 q^{52} + 690 q^{53} - 128 q^{54} + 1432 q^{55} + 160 q^{56} - 1312 q^{57} + 296 q^{58} + 1136 q^{59} + 16 q^{60} - 642 q^{61} - 848 q^{62} + 420 q^{63} + 384 q^{64} - 2256 q^{65} - 96 q^{66} + 426 q^{67} + 112 q^{68} + 276 q^{69} + 160 q^{70} - 1308 q^{71} - 512 q^{72} - 980 q^{73} + 220 q^{74} - 4432 q^{75} + 152 q^{76} + 216 q^{77} + 640 q^{78} + 1948 q^{79} - 160 q^{80} + 4454 q^{81} + 1016 q^{82} + 2146 q^{83} - 1040 q^{84} + 1636 q^{85} + 1380 q^{86} - 2596 q^{87} - 752 q^{88} - 1044 q^{89} - 4804 q^{90} - 1956 q^{91} + 3804 q^{93} + 1008 q^{94} + 2648 q^{95} - 128 q^{96} - 428 q^{97} + 832 q^{98} + 2586 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(46))\) 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 23
46.4.a.a 46.a 1.a $1$ $2.714$ \(\Q\) None \(-2\) \(-1\) \(-10\) \(-12\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\cdots\)
46.4.a.b 46.a 1.a $1$ $2.714$ \(\Q\) None \(2\) \(-9\) \(-20\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-9q^{3}+4q^{4}-20q^{5}-18q^{6}+\cdots\)
46.4.a.c 46.a 1.a $2$ $2.714$ \(\Q(\sqrt{41}) \) None \(-4\) \(-1\) \(10\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
46.4.a.d 46.a 1.a $2$ $2.714$ \(\Q(\sqrt{73}) \) None \(4\) \(3\) \(10\) \(12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(46)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)