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Properties

Label 95.6.a
Level $95$
Weight $6$
Character orbit 95.a
Rep. character $\chi_{95}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $5$
Sturm bound $60$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 95.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(95))\).

Total New Old
Modular forms 52 30 22
Cusp forms 48 30 18
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.

\(5\)\(19\)FrickeDim
\(+\)\(+\)$+$\(6\)
\(+\)\(-\)$-$\(10\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(19\)

Trace form

\( 30 q + 4 q^{2} + 524 q^{4} - 50 q^{5} - 148 q^{6} - 196 q^{7} + 624 q^{8} + 2590 q^{9} + O(q^{10}) \) \( 30 q + 4 q^{2} + 524 q^{4} - 50 q^{5} - 148 q^{6} - 196 q^{7} + 624 q^{8} + 2590 q^{9} + 1232 q^{11} - 608 q^{12} + 404 q^{13} - 1296 q^{14} + 1100 q^{15} + 5668 q^{16} - 868 q^{17} + 6708 q^{18} + 1400 q^{20} - 3072 q^{21} - 6032 q^{22} - 6084 q^{23} + 3308 q^{24} + 18750 q^{25} + 7868 q^{26} + 15516 q^{27} + 28932 q^{28} - 644 q^{29} - 5400 q^{30} - 12568 q^{31} + 7592 q^{32} + 32516 q^{33} + 40704 q^{34} - 6700 q^{35} + 39192 q^{36} + 27544 q^{37} - 8664 q^{38} + 36736 q^{39} - 2380 q^{41} + 21180 q^{42} - 54956 q^{43} + 12936 q^{44} + 5550 q^{45} - 5624 q^{46} - 42460 q^{47} - 97804 q^{48} + 52838 q^{49} + 2500 q^{50} + 68376 q^{51} - 29164 q^{52} + 35728 q^{53} - 176772 q^{54} + 7400 q^{55} - 103592 q^{56} - 12996 q^{57} - 72852 q^{58} + 76016 q^{59} + 78100 q^{60} + 100900 q^{61} - 265832 q^{62} + 30636 q^{63} + 148468 q^{64} - 43800 q^{65} - 199912 q^{66} + 8204 q^{67} - 356516 q^{68} - 270304 q^{69} + 7000 q^{70} + 52416 q^{71} + 224500 q^{72} - 26036 q^{73} + 162592 q^{74} - 72672 q^{77} - 107912 q^{78} + 361664 q^{79} + 7800 q^{80} - 303154 q^{81} + 93728 q^{82} + 83276 q^{83} - 520736 q^{84} - 48500 q^{85} - 171248 q^{86} - 271896 q^{87} - 751684 q^{88} + 57084 q^{89} + 271552 q^{91} - 530692 q^{92} + 98904 q^{93} + 46688 q^{94} - 72200 q^{95} + 500060 q^{96} - 151472 q^{97} + 286468 q^{98} + 524368 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(95))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 19
95.6.a.a 95.a 1.a $1$ $15.236$ \(\Q\) None \(-7\) \(-11\) \(-25\) \(-197\) $+$ $-$ $\mathrm{SU}(2)$ \(q-7q^{2}-11q^{3}+17q^{4}-5^{2}q^{5}+77q^{6}+\cdots\)
95.6.a.b 95.a 1.a $5$ $15.236$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-7\) \(-16\) \(125\) \(-312\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-4+\beta _{1}+\beta _{4})q^{3}+\cdots\)
95.6.a.c 95.a 1.a $6$ $15.236$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(5\) \(-20\) \(-150\) \(-80\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-3+\beta _{4})q^{3}+(9-2\beta _{1}+\cdots)q^{4}+\cdots\)
95.6.a.d 95.a 1.a $9$ $15.236$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(4\) \(9\) \(-225\) \(313\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(18+\beta _{2})q^{4}+\cdots\)
95.6.a.e 95.a 1.a $9$ $15.236$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(38\) \(225\) \(80\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(4+\beta _{3})q^{3}+(23-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(95))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(95)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)