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Properties

Label 95.11.f
Level $95$
Weight $11$
Character orbit 95.f
Rep. character $\chi_{95}(58,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $180$
Newform subspaces $1$
Sturm bound $110$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(110\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(95, [\chi])\).

Total New Old
Modular forms 204 180 24
Cusp forms 196 180 16
Eisenstein series 8 0 8

Trace form

\( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8} + O(q^{10}) \) \( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8} + 322576 q^{10} + 435480 q^{11} - 1494224 q^{12} - 48556 q^{13} + 4094384 q^{15} - 44262960 q^{16} - 505646 q^{17} - 6298560 q^{18} + 24709120 q^{20} + 38659000 q^{21} - 34179888 q^{22} - 16720612 q^{23} + 33791178 q^{25} + 86813120 q^{26} - 14436244 q^{27} - 133340704 q^{28} + 232195960 q^{30} + 64155640 q^{31} + 226208632 q^{32} + 11350832 q^{33} - 151622642 q^{35} + 1852895600 q^{36} - 373035252 q^{37} + 28746456 q^{40} - 461563640 q^{41} + 1629657056 q^{42} - 123615382 q^{43} - 1310415408 q^{45} - 462362320 q^{46} + 1397297450 q^{47} + 1422934764 q^{48} - 903150292 q^{50} + 786433560 q^{51} + 1822166628 q^{52} + 3614315976 q^{53} + 1190412472 q^{55} - 2951801640 q^{56} - 2958059232 q^{58} + 13343296716 q^{60} + 1705662680 q^{61} + 5674658712 q^{62} - 2955158450 q^{63} + 5908753192 q^{65} - 6577823720 q^{66} - 4198675868 q^{67} - 10832391640 q^{68} + 7095849220 q^{70} + 5547444200 q^{71} + 12902115940 q^{72} + 331620970 q^{73} - 11862069968 q^{75} - 10562822066 q^{77} - 12446121128 q^{78} + 9866450160 q^{80} - 63545444700 q^{81} + 9916048472 q^{82} - 1670597036 q^{83} - 25420912412 q^{85} - 54497853920 q^{86} + 20560091976 q^{87} - 4241912244 q^{88} + 1724884384 q^{90} - 9777438680 q^{91} + 57824442424 q^{92} + 49325339272 q^{93} - 5501891978 q^{95} - 7492787400 q^{96} - 74779609888 q^{97} - 60964218864 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.11.f.a 95.f 5.c $180$ $60.359$ None \(-64\) \(-124\) \(8454\) \(32890\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{11}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(95, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)