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Properties

Label 140.15.l
Level $140$
Weight $15$
Character orbit 140.l
Rep. character $\chi_{140}(57,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $84$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 140.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(140, [\chi])\).

Total New Old
Modular forms 684 84 600
Cusp forms 660 84 576
Eisenstein series 24 0 24

Trace form

\( 84 q + 4316 q^{3} + 32248 q^{5} + O(q^{10}) \) \( 84 q + 4316 q^{3} + 32248 q^{5} - 7461804 q^{11} - 266789676 q^{13} + 398589152 q^{15} + 174890028 q^{17} - 945427364 q^{21} - 11101794320 q^{23} + 7968920792 q^{25} - 13986917308 q^{27} - 46264750304 q^{31} + 270620242492 q^{33} + 182556468736 q^{37} + 67284398384 q^{41} - 805234432852 q^{43} + 1526128599332 q^{45} + 2006708680348 q^{47} - 2385505868804 q^{51} - 488863969924 q^{53} - 715258021804 q^{55} + 1782488311220 q^{57} + 2348389476312 q^{61} - 4679819333392 q^{63} - 12934071084184 q^{65} - 1822136157660 q^{67} - 25160566370512 q^{71} - 34661376699696 q^{73} - 13871420321812 q^{75} + 8193995904584 q^{77} - 265925764832076 q^{81} - 166462619231424 q^{83} - 55102331344428 q^{85} + 22238642389012 q^{87} - 59680978602252 q^{91} + 344601540010124 q^{93} + 254628277023796 q^{95} - 56916396340228 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.15.l.a 140.l 5.c $84$ $174.061$ None \(0\) \(4316\) \(32248\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{15}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)