LMFDB - Space of modular forms of level 95, weight 2, and Character 95.e

Defining parameters

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 19 $
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$ 3 $
Sturm bound:			$20$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(95, [\chi])$.

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

Trace form

$ 16 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 4 q^{6} - 12 q^{7} + 12 q^{8} - 6 q^{9} + O(q^{10}) $

\( 16 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 4 q^{6} - 12 q^{7} + 12 q^{8} - 6 q^{9} - 8 q^{11} + 12 q^{12} + 6 q^{13} - 6 q^{14} - 4 q^{15} - 14 q^{16} - 6 q^{17} + 8 q^{18} - 2 q^{19} + 8 q^{21} + 6 q^{22} - 6 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} + 16 q^{27} + 6 q^{29} + 16 q^{30} - 16 q^{31} - 24 q^{32} - 24 q^{33} + 10 q^{34} + 2 q^{35} + 6 q^{36} + 8 q^{37} - 6 q^{38} + 12 q^{39} - 18 q^{40} + 16 q^{41} + 38 q^{42} + 4 q^{43} + 36 q^{44} - 8 q^{45} - 24 q^{46} - 16 q^{48} - 16 q^{49} + 4 q^{50} - 4 q^{51} + 42 q^{52} + 24 q^{54} - 52 q^{56} - 28 q^{57} - 68 q^{58} + 14 q^{59} - 6 q^{60} + 4 q^{61} - 24 q^{62} - 2 q^{63} + 80 q^{64} + 40 q^{65} + 2 q^{66} + 14 q^{67} + 76 q^{68} - 28 q^{69} + 8 q^{70} + 12 q^{71} - 28 q^{72} + 34 q^{73} - 18 q^{74} + 4 q^{75} + 46 q^{76} - 28 q^{77} - 12 q^{78} + 2 q^{79} + 20 q^{81} - 52 q^{82} + 20 q^{83} - 128 q^{84} + 8 q^{85} + 24 q^{86} + 4 q^{87} - 32 q^{88} + 18 q^{89} + 24 q^{90} + 12 q^{91} - 40 q^{92} - 12 q^{93} - 20 q^{94} - 12 q^{95} + 76 q^{96} - 16 q^{97} - 32 q^{98} - 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(95, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
95.2.e.a	$2$	$0.759$	$\Q(\sqrt{-3}) $	None	$0$	$2$	$1$	$-8$	$q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
95.2.e.b	$6$	$0.759$	6.0.3518667.1	None	$-1$	$-1$	$3$	$4$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots$
95.2.e.c	$8$	$0.759$	8.0.4601315889.1	None	$-1$	$-3$	$-4$	$-8$	$q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$

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Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	95.2.e

Level	$95$
Weight	$2$
Character orbit	95.e
Rep. character	$\chi_{95}(11,\cdot)$
Character field	$\Q(\zeta_{3})$
Dimension	$16$
Newform subspaces	$3$
Sturm bound	$20$
Trace bound	$1$

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
95.2.e.a	$2$	$0.759$	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(2\)	\(1\)	\(-8\)	\(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
95.2.e.b	$6$	$0.759$	6.0.3518667.1	None	\(-1\)	\(-1\)	\(3\)	\(4\)	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
95.2.e.c	$8$	$0.759$	8.0.4601315889.1	None	\(-1\)	\(-3\)	\(-4\)	\(-8\)	\(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)