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Properties

Label 45.21.g
Level $45$
Weight $21$
Character orbit 45.g
Rep. character $\chi_{45}(28,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $98$
Newform subspaces $3$
Sturm bound $126$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 45.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(126\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(45, [\chi])\).

Total New Old
Modular forms 248 102 146
Cusp forms 232 98 134
Eisenstein series 16 4 12

Trace form

\( 98 q + 2 q^{2} - 7302136 q^{5} + 332228048 q^{7} + 925919400 q^{8} + O(q^{10}) \) \( 98 q + 2 q^{2} - 7302136 q^{5} + 332228048 q^{7} + 925919400 q^{8} + 14113914854 q^{10} - 3794609096 q^{11} - 128137981402 q^{13} - 26920433441872 q^{16} + 723885655502 q^{17} - 7654503172344 q^{20} - 134129828311904 q^{22} + 132607993477952 q^{23} + 343582624819046 q^{25} - 49865327269316 q^{26} + 1035591372150952 q^{28} - 841812441868304 q^{31} + 2470441266427652 q^{32} - 1282471888550680 q^{35} - 11563502203290502 q^{37} - 7484065153775400 q^{38} - 62214990873436092 q^{40} - 28972531224558176 q^{41} + 31357003244095448 q^{43} + 164111721862119976 q^{46} + 171573437008053752 q^{47} + 335043239949236366 q^{50} - 572839696724637052 q^{52} + 239946316031305202 q^{53} - 971854401161478584 q^{55} - 727951064798554800 q^{56} - 219167424217467600 q^{58} + 150896270506529416 q^{61} - 980047740600047696 q^{62} - 4167358952618768158 q^{65} + 6954740753544729848 q^{67} + 83179720002654748 q^{68} + 642554596235792760 q^{70} + 6797045574120451984 q^{71} - 1647672121406485702 q^{73} - 31991001008152672800 q^{76} - 17432521574128659296 q^{77} + 21478995310361303756 q^{80} - 76143215942505207104 q^{82} - 46584570975824914048 q^{83} + 9799700311323238022 q^{85} - 56936652741474901496 q^{86} + 97562895021620155200 q^{88} + 288865857607995156976 q^{91} + 166522963229244360752 q^{92} + 86554755435154520376 q^{95} + 36492456609014749898 q^{97} - 70889126794143827702 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.21.g.a 45.g 5.c $18$ $114.081$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(7302140\) \(-585532752\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(579418\beta _{1}-2^{5}\beta _{2}+2^{5}\beta _{3}+\cdots)q^{4}+\cdots\)
45.21.g.b 45.g 5.c $40$ $114.081$ None \(0\) \(0\) \(-14604276\) \(712185100\) $\mathrm{SU}(2)[C_{4}]$
45.21.g.c 45.g 5.c $40$ $114.081$ None \(0\) \(0\) \(0\) \(205575700\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{21}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{21}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)