Properties

Label 25.36.b
Level $25$
Weight $36$
Character orbit 25.b
Rep. character $\chi_{25}(24,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $4$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 25.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(25, [\chi])\).

Total New Old
Modular forms 90 54 36
Cusp forms 84 52 32
Eisenstein series 6 2 4

Trace form

\( 52 q - 952681885426 q^{4} + 115202673551914 q^{6} - 663191408165380444 q^{9} + O(q^{10}) \) \( 52 q - 952681885426 q^{4} + 115202673551914 q^{6} - 663191408165380444 q^{9} + 4364872380387591704 q^{11} - 170028140507178713892 q^{14} + 13745028206935094942722 q^{16} - 16569636988350734247560 q^{19} - 158569698235105900818576 q^{21} - 17117337726226645681866030 q^{24} + 15864080436140643199933184 q^{26} - 128554051154105379609123640 q^{29} + 233356342279295667115213904 q^{31} + 2053891592977340619334499598 q^{34} + 7403507680507885580613496772 q^{36} + 1722210081516724394569134352 q^{39} + 34661321391947885326476647104 q^{41} - 276534776435102091244543390402 q^{44} - 346041774330913672286208150996 q^{46} - 3944234673017111750254660509636 q^{49} + 3354072579506976352631447167144 q^{51} - 18438681502733495693516367676510 q^{54} - 4817739472093679108286688380660 q^{56} - 74581895177980413326362597167680 q^{59} + 48507441429554818237365150889304 q^{61} - 270278530375073141797239314956066 q^{64} - 65974748597465284563935795731222 q^{66} + 467455407404138537024858029221312 q^{69} + 1243616410265536196133903401431504 q^{71} + 1194731648693783245870172102665028 q^{74} - 360791935902655825485366998447470 q^{76} + 5786749246111080783705478838964160 q^{79} + 9892175287071004846810467969965812 q^{81} + 22418598950530256561156801897840988 q^{84} + 5747105980621041336730163749694744 q^{86} - 42767182627981881132826793553209520 q^{89} + 373447141187796411361304660527744 q^{91} - 236698807603921736295026318357011032 q^{94} + 111523361885496650161141412520214814 q^{96} + 91494718480880715253566494733388912 q^{99} + O(q^{100}) \)

Decomposition of \(S_{36}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.36.b.a 25.b 5.b $6$ $193.988$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(186\beta _{1}-\beta _{2})q^{2}+(139834\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.36.b.b 25.b 5.b $10$ $193.988$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(15\beta _{5}+\beta _{6})q^{2}+(-8312\beta _{5}-204\beta _{6}+\cdots)q^{3}+\cdots\)
25.36.b.c 25.b 5.b $12$ $193.988$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(214\beta _{1}-1573\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots\)
25.36.b.d 25.b 5.b $24$ $193.988$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{36}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{36}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{36}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)