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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
15.10.a.a \(1\) \(7.726\) \(\Q\) None \(-4\) \(81\) \(625\) \(-7680\) \(-\) \(-\) \(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
15.10.a.b \(1\) \(7.726\) \(\Q\) None \(22\) \(-81\) \(-625\) \(-5988\) \(+\) \(+\) \(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
15.10.a.c \(2\) \(7.726\) \(\Q(\sqrt{4729}) \) None \(19\) \(162\) \(-1250\) \(-11872\) \(-\) \(+\) \(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
15.10.a.d \(2\) \(7.726\) \(\Q(\sqrt{241}) \) None \(31\) \(-162\) \(1250\) \(14112\) \(+\) \(-\) \(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)

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

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