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Properties

Label 15.4.a
Level $15$
Weight $4$
Character orbit 15.a
Rep. character $\chi_{15}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $8$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(15))\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
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.

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(0\)

Trace form

\( 2 q + 4 q^{2} - 6 q^{4} - 6 q^{6} - 4 q^{7} - 36 q^{8} + 18 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{2} - 6 q^{4} - 6 q^{6} - 4 q^{7} - 36 q^{8} + 18 q^{9} - 10 q^{10} + 28 q^{11} - 24 q^{12} + 96 q^{13} + 36 q^{14} + 30 q^{15} - 30 q^{16} + 40 q^{17} + 36 q^{18} - 144 q^{19} - 40 q^{20} - 132 q^{21} - 20 q^{22} - 288 q^{23} + 18 q^{24} + 50 q^{25} + 244 q^{26} + 188 q^{28} + 152 q^{29} + 60 q^{30} - 88 q^{31} + 116 q^{32} + 228 q^{33} + 148 q^{34} - 220 q^{35} - 54 q^{36} - 104 q^{37} - 392 q^{38} - 156 q^{39} + 30 q^{40} + 452 q^{41} - 252 q^{42} - 96 q^{43} - 388 q^{44} - 528 q^{46} + 232 q^{47} + 336 q^{48} + 290 q^{49} + 100 q^{50} - 204 q^{51} - 80 q^{52} + 112 q^{53} - 54 q^{54} + 380 q^{55} - 60 q^{56} + 312 q^{57} - 4 q^{58} + 124 q^{59} - 90 q^{60} + 420 q^{61} + 312 q^{62} - 36 q^{63} + 266 q^{64} - 260 q^{65} + 372 q^{66} - 280 q^{67} + 152 q^{68} - 144 q^{69} - 420 q^{70} - 616 q^{71} - 324 q^{72} - 468 q^{73} - 244 q^{74} + 16 q^{76} - 1728 q^{77} - 600 q^{78} - 760 q^{79} + 560 q^{80} + 162 q^{81} + 1112 q^{82} + 1368 q^{83} + 444 q^{84} - 340 q^{85} + 88 q^{86} + 924 q^{87} - 276 q^{88} + 1356 q^{89} - 90 q^{90} + 952 q^{91} + 1056 q^{92} - 1464 q^{93} + 184 q^{94} + 520 q^{95} + 618 q^{96} + 580 q^{97} + 404 q^{98} + 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(15))\) 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
15.4.a.a 15.a 1.a $1$ $0.885$ \(\Q\) None \(1\) \(3\) \(5\) \(-24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b 15.a 1.a $1$ $0.885$ \(\Q\) None \(3\) \(-3\) \(-5\) \(20\) $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces

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