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Properties

Label 15.10.a
Level $15$
Weight $10$
Character orbit 15.a
Rep. character $\chi_{15}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 15.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(15))\).

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.

\(3\)\(5\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\( 6 q + 68 q^{2} + 1538 q^{4} - 3078 q^{6} - 11428 q^{7} + 67932 q^{8} + 39366 q^{9} + O(q^{10}) \) \( 6 q + 68 q^{2} + 1538 q^{4} - 3078 q^{6} - 11428 q^{7} + 67932 q^{8} + 39366 q^{9} - 8750 q^{10} - 87076 q^{11} + 41472 q^{12} + 55888 q^{13} + 115452 q^{14} - 101250 q^{15} + 1085330 q^{16} - 420520 q^{17} + 446148 q^{18} + 658912 q^{19} - 905000 q^{20} - 2241756 q^{21} - 7156540 q^{22} + 3122496 q^{23} + 3193506 q^{24} + 2343750 q^{25} - 5892868 q^{26} + 3780524 q^{28} - 6996536 q^{29} - 1620000 q^{30} - 4504264 q^{31} + 17859412 q^{32} - 1195236 q^{33} + 5709836 q^{34} + 15182500 q^{35} + 10090818 q^{36} + 25085112 q^{37} - 2385976 q^{38} - 5547852 q^{39} - 4751250 q^{40} + 24274636 q^{41} - 44096724 q^{42} - 4089728 q^{43} - 102869396 q^{44} - 90064944 q^{46} + 51128264 q^{47} + 65192688 q^{48} + 84594310 q^{49} + 26562500 q^{50} + 62822628 q^{51} - 52677360 q^{52} - 114062224 q^{53} - 20194758 q^{54} - 80472500 q^{55} - 68883420 q^{56} - 2667816 q^{57} - 205991852 q^{58} + 180942428 q^{59} - 130916250 q^{60} + 479495740 q^{61} - 31830936 q^{62} - 74979108 q^{63} + 464210442 q^{64} - 192047500 q^{65} - 57426084 q^{66} - 484354360 q^{67} + 717440536 q^{68} + 5244912 q^{69} + 543322500 q^{70} + 83143192 q^{71} + 445701852 q^{72} - 591042044 q^{73} - 773558108 q^{74} - 849378912 q^{76} + 72064224 q^{77} + 265485600 q^{78} - 274527880 q^{79} + 103030000 q^{80} + 258280326 q^{81} + 1526220184 q^{82} + 804884184 q^{83} - 1559325492 q^{84} - 192897500 q^{85} - 752029576 q^{86} + 37145628 q^{87} - 2168339028 q^{88} - 329760348 q^{89} - 57408750 q^{90} - 871611944 q^{91} - 2807106528 q^{92} - 830087352 q^{93} + 3271510568 q^{94} + 363665000 q^{95} + 2378839914 q^{96} + 1387556460 q^{97} + 5935831732 q^{98} - 571305636 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(15))\) 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
15.10.a.a 15.a 1.a $1$ $7.726$ \(\Q\) None \(-4\) \(81\) \(625\) \(-7680\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
15.10.a.b 15.a 1.a $1$ $7.726$ \(\Q\) None \(22\) \(-81\) \(-625\) \(-5988\) $+$ $+$ $\mathrm{SU}(2)$ \(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
15.10.a.c 15.a 1.a $2$ $7.726$ \(\Q(\sqrt{4729}) \) None \(19\) \(162\) \(-1250\) \(-11872\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
15.10.a.d 15.a 1.a $2$ $7.726$ \(\Q(\sqrt{241}) \) None \(31\) \(-162\) \(1250\) \(14112\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)