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Properties

Label 35.23.d
Level $35$
Weight $23$
Character orbit 35.d
Rep. character $\chi_{35}(6,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $1$
Sturm bound $92$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 23 \)
Character orbit: \([\chi]\) \(=\) 35.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(92\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(35, [\chi])\).

Total New Old
Modular forms 90 60 30
Cusp forms 86 60 26
Eisenstein series 4 0 4

Trace form

\( 60 q + 3082 q^{2} + 135428954 q^{4} - 3055909130 q^{7} + 25377678038 q^{8} - 661372200146 q^{9} + O(q^{10}) \) \( 60 q + 3082 q^{2} + 135428954 q^{4} - 3055909130 q^{7} + 25377678038 q^{8} - 661372200146 q^{9} + 421589555950 q^{11} - 8699235238658 q^{14} - 1566308593750 q^{15} + 369627834003746 q^{16} + 415928127797438 q^{18} - 1078202496509598 q^{21} - 1289863373276728 q^{22} + 2057765855851708 q^{23} - 28610229492187500 q^{25} - 5312463395289722 q^{28} + 3608893668838954 q^{29} + 5455600000000000 q^{30} - 234000910493039706 q^{32} + 15924480761718750 q^{35} - 2640248785355912910 q^{36} + 655583832693557372 q^{37} + 985820193149982114 q^{39} - 464348397378619620 q^{42} - 5028896433479750872 q^{43} - 4811158551990331212 q^{44} + 5829498897608948996 q^{46} + 10052726682873168192 q^{49} - 1469612121582031250 q^{50} - 1544116318745644866 q^{51} + 51620459328740027440 q^{53} + 67262697481314575186 q^{56} - 25333193766053084340 q^{57} - 97155762723020036272 q^{58} + 99301388665429687500 q^{60} - 187478216072941877270 q^{63} + 1171118054568504844018 q^{64} + 193120148494628906250 q^{65} + 17606512353408349152 q^{67} - 423966980353125000000 q^{70} + 1749206412727178653000 q^{71} + 2051159457561636077902 q^{72} - 718003528022569449196 q^{74} - 3010944355049882410688 q^{77} + 1707453747839507312100 q^{78} - 937557688164930689766 q^{79} + 8104625356763229494224 q^{81} + 514114619192192024712 q^{84} - 834804501538183593750 q^{85} + 493000733261595713396 q^{86} - 4527549735975001009076 q^{88} - 4793472309882262867518 q^{91} - 26497769453932870509756 q^{92} - 37607585969580599149620 q^{93} - 848541054023437500000 q^{95} + 24540046972262999691058 q^{98} - 12620729146062134780812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.23.d.a 35.d 7.b $60$ $107.348$ None \(3082\) \(0\) \(0\) \(-3055909130\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{23}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{23}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{23}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)