Properties

Label 95.11.d
Level $95$
Weight $11$
Character orbit 95.d
Rep. character $\chi_{95}(94,\cdot)$
Character field $\Q$
Dimension $98$
Newform subspaces $4$
Sturm bound $110$
Trace bound $5$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 102 102 0
Cusp forms 98 98 0
Eisenstein series 4 4 0

Trace form

\( 98 q + 50368 q^{4} + 1109 q^{5} + 760 q^{6} + 1850198 q^{9} + O(q^{10}) \) \( 98 q + 50368 q^{4} + 1109 q^{5} + 760 q^{6} + 1850198 q^{9} - 130594 q^{11} + 23321368 q^{16} + 1528858 q^{19} + 6645180 q^{20} + 44844320 q^{24} - 8375915 q^{25} + 40029520 q^{26} - 45441744 q^{30} - 116436889 q^{35} + 973007168 q^{36} + 134353720 q^{39} - 1010104704 q^{44} - 160483077 q^{45} - 3999481056 q^{49} + 841666800 q^{54} - 1168252963 q^{55} - 1029741434 q^{61} + 7397052168 q^{64} - 3543457560 q^{66} - 14144890080 q^{74} + 18081554088 q^{76} + 10812290056 q^{80} + 38605570578 q^{81} - 11624327715 q^{85} - 1965704127 q^{95} + 12794582240 q^{96} - 83582806574 q^{99} + O(q^{100}) \)

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.d.a 95.d 95.d $2$ $60.359$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(3951\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{10}q^{4}+(2026+101\beta )q^{5}+(177+\cdots)q^{7}+\cdots\)
95.11.d.b 95.d 95.d $4$ $60.359$ 4.4.462080.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(-12500\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+12\beta _{2})q^{2}+(-23\beta _{1}+43\beta _{2}+\cdots)q^{3}+\cdots\)
95.11.d.c 95.d 95.d $4$ $60.359$ 4.4.7600.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(12500\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+2\beta _{2})q^{2}+(-6\beta _{1}+17\beta _{2})q^{3}+\cdots\)
95.11.d.d 95.d 95.d $88$ $60.359$ None \(0\) \(0\) \(-2842\) \(0\) $\mathrm{SU}(2)[C_{2}]$