Properties

Label 15.8.a
Level 15
Weight 8
Character orbit a
Rep. character \(\chi_{15}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 3
Sturm bound 16
Trace bound 2

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 15.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(15))\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
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.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\( 4q - 28q^{2} + 54q^{3} + 466q^{4} - 54q^{6} + 2264q^{7} - 2436q^{8} + 2916q^{9} + O(q^{10}) \) \( 4q - 28q^{2} + 54q^{3} + 466q^{4} - 54q^{6} + 2264q^{7} - 2436q^{8} + 2916q^{9} + 5250q^{10} - 2800q^{11} + 10368q^{12} - 11488q^{13} - 20964q^{14} + 6750q^{15} + 20338q^{16} - 32032q^{17} - 20412q^{18} - 33712q^{19} - 41000q^{20} - 13392q^{21} - 19644q^{22} + 170088q^{23} - 126846q^{24} + 62500q^{25} + 347708q^{26} + 39366q^{27} - 165748q^{28} + 477616q^{29} + 54000q^{30} + 46832q^{31} - 1063916q^{32} + 102816q^{33} + 54012q^{34} + 43000q^{35} + 339714q^{36} - 153616q^{37} - 769432q^{38} - 769500q^{39} + 666750q^{40} + 375592q^{41} + 402732q^{42} - 421000q^{43} - 2040596q^{44} + 922272q^{46} + 1210520q^{47} + 1626480q^{48} + 579204q^{49} - 437500q^{50} - 325188q^{51} - 2146192q^{52} + 1575488q^{53} - 39366q^{54} + 1212000q^{55} + 5773380q^{56} - 3136968q^{57} - 2186604q^{58} - 2288608q^{59} - 830250q^{60} - 4545304q^{61} + 5573928q^{62} + 1650456q^{63} + 10293082q^{64} - 811000q^{65} - 2849796q^{66} - 5036632q^{67} - 9434504q^{68} + 49896q^{69} - 445500q^{70} - 2625392q^{71} - 1775844q^{72} + 2617208q^{73} - 3041564q^{74} + 843750q^{75} - 13374352q^{76} + 6733248q^{77} + 15359328q^{78} + 3505280q^{79} - 8666000q^{80} + 2125764q^{81} + 13003128q^{82} - 17321256q^{83} - 7530516q^{84} + 2631000q^{85} + 13624760q^{86} + 5724324q^{87} + 23149164q^{88} + 12431928q^{89} + 3827250q^{90} - 3365648q^{91} + 15479424q^{92} + 4277664q^{93} - 32795880q^{94} - 8182000q^{95} - 34913862q^{96} + 11522888q^{97} - 21248492q^{98} - 2041200q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(15))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
15.8.a.a \(1\) \(4.686\) \(\Q\) None \(-22\) \(27\) \(-125\) \(-420\) \(-\) \(+\) \(q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.b \(1\) \(4.686\) \(\Q\) None \(-13\) \(-27\) \(-125\) \(1380\) \(+\) \(+\) \(q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.c \(2\) \(4.686\) \(\Q(\sqrt{601}) \) None \(7\) \(54\) \(250\) \(1304\) \(-\) \(-\) \(q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)