Newform orbit 1007.2.a.d

• Label: 1007.2.a.d
• Level: $1007$
• Weight: $2$
• Character orbit: 1007.a
• Self dual: yes
• Analytic conductor: $8.041$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1007 = 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1007.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(8.04093548354\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 6 q^{2} + 9 q^{3} + 32 q^{4} + 4 q^{5} - 3 q^{6} + 8 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.65639			2.84015			5.05643			−0.336491			−7.54455			3.03688			−8.11907			5.06644			0.893852
1.2	−2.46294			−0.150714			4.06608			−3.58238			0.371201			1.46744			−5.08862			−2.97729			8.82319
1.3	−2.32557			−2.53410			3.40826			0.686202			5.89322			−1.86757			−3.27499			3.42167			−1.59581
1.4	−2.08816			1.04393			2.36041			2.84133			−2.17990			2.53269			−0.752603			−1.91020			−5.93315
1.5	−1.92126			−0.416837			1.69123			3.83474			0.800852			−4.84972			0.593229			−2.82625			−7.36752
1.6	−1.80505			2.98371			1.25820			−0.549772			−5.38574			−4.91564			1.33899			5.90253			0.992364
1.7	−1.63043			−0.873124			0.658301			−1.37408			1.42357			0.0644218			2.18755			−2.23765			2.24034
1.8	−1.08823			1.10712			−0.815766			−3.30422			−1.20479			4.22827			3.06419			−1.77429			3.59574
1.9	−1.05499			−2.22764			−0.886999			0.509126			2.35013			4.68545			3.04575			1.96238			−0.537122
1.10	−0.608659			2.55305			−1.62953			1.10594			−1.55394			0.514046			2.20915			3.51806			−0.673139
1.11	0.0161975			0.428843			−1.99974			4.35358			0.00694617			2.10533			−0.0647856			−2.81609			0.0705169
1.12	0.182159			0.171419			−1.96682			−0.333807			0.0312256			−2.26177			−0.722592			−2.97062			−0.0608060
1.13	0.273006			3.10897			−1.92547			2.95116			0.848768			3.60587			−1.07168			6.66571			0.805683
1.14	0.359850			−1.00392			−1.87051			−4.00398			−0.361259			−3.14633			−1.39280			−1.99215			−1.44083
1.15	0.784014			2.28561			−1.38532			−4.31184			1.79195			1.30295			−2.65414			2.22400			−3.38054
1.16	0.853371			−2.63008			−1.27176			−1.39064			−2.24444			−3.80870			−2.79202			3.91734			−1.18673
1.17	1.29003			−2.42689			−0.335830			−3.76625			−3.13075			2.92073			−3.01328			2.88979			−4.85856
1.18	1.53692			2.90429			0.362110			−0.734427			4.46365			3.29613			−2.51730			5.43489			−1.12875
1.19	1.77418			1.38953			1.14772			3.60012			2.46528			−2.55165			−1.51210			−1.06921			6.38726
1.20	1.83567			−2.34430			1.36969			2.08339			−4.30337			−0.327981			−1.15704			2.49575			3.82443

Atkin-Lehner signs

\( p \)	Sign
\(19\)	\(-1\)
\(53\)	\(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1007.2.a.d	✓	26
3.b	odd	2	1		9063.2.a.q		26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1007.2.a.d	✓	26	1.a	even	1	1	trivial
9063.2.a.q		26	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^26 - 6*T2^25 - 24*T2^24 + 204*T2^23 + 143*T2^22 - 2957*T2^21 + 1313*T2^20 + 23773*T2^19 - 25728*T2^18 - 115036*T2^17 + 181081*T2^16 + 336456*T2^15 - 713409*T2^14 - 543569*T2^13 + 1698815*T2^12 + 280790*T2^11 - 2424843*T2^10 + 511527*T2^9 + 1923915*T2^8 - 940458*T2^7 - 679950*T2^6 + 547980*T2^5 + 10922*T2^4 - 95345*T2^3 + 27015*T2^2 - 2450*T2 + 33