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Properties

Label 15.11.f
Level $15$
Weight $11$
Character orbit 15.f
Rep. character $\chi_{15}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(15, [\chi])\).

Total New Old
Modular forms 44 20 24
Cusp forms 36 20 16
Eisenstein series 8 0 8

Trace form

\( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8} + O(q^{10}) \) \( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8} + 153704 q^{10} + 32080 q^{11} - 620136 q^{12} - 69352 q^{13} + 662904 q^{15} - 3111700 q^{16} + 347360 q^{17} - 1259712 q^{18} + 24132564 q^{20} + 1448280 q^{21} - 27255980 q^{22} - 30995704 q^{23} + 36824936 q^{25} + 80977840 q^{26} - 104897636 q^{28} - 6436584 q^{30} - 8846480 q^{31} - 81249676 q^{32} + 86048244 q^{33} + 91578920 q^{35} + 177540660 q^{36} - 27635896 q^{37} + 44187744 q^{38} - 887009352 q^{40} + 149264920 q^{41} + 442105452 q^{42} + 675552392 q^{43} - 183996684 q^{45} - 1916100680 q^{46} - 257112832 q^{47} + 1182772368 q^{48} + 909704384 q^{50} - 711183240 q^{51} + 1397512520 q^{52} - 152646064 q^{53} - 1181518004 q^{55} + 1735516800 q^{56} + 342507528 q^{57} - 1947576252 q^{58} - 1084331124 q^{60} + 2582791000 q^{61} - 969372632 q^{62} + 208718532 q^{63} + 7250334488 q^{65} - 1968290280 q^{66} - 6731030200 q^{67} - 12869460704 q^{68} + 7421027700 q^{70} + 7511442640 q^{71} + 786296484 q^{72} + 1660222316 q^{73} + 72454824 q^{75} + 9998646360 q^{76} - 13264676792 q^{77} - 5574993480 q^{78} - 15692039116 q^{80} - 7748409780 q^{81} + 27089146528 q^{82} + 30753878864 q^{83} - 2653017808 q^{85} - 46532117120 q^{86} + 3048661476 q^{87} + 5813201532 q^{88} + 8161910244 q^{90} + 14175275920 q^{91} + 30045377384 q^{92} - 6062778072 q^{93} - 58265269776 q^{95} - 18513718020 q^{96} - 32149992820 q^{97} + 54432471592 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.11.f.a 15.f 5.c $20$ $9.530$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-64\) \(0\) \(10676\) \(10604\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)